UNIVERSITY  OF  CALIFORNIA 
SAN  FRANCISCO  LIBRARY 


PRINCIPLES 


OF 


PHYSICS    AND    METEOROLOGY. 


TatS. 


7.  Sindairslvflt 


PRINCIPLES 


OF 


PHYSICS  AND  METEOROLOGY, 


BY    J.    MULLEK, 

PROFESSOR  OF  PHYSICS  AT  THE  UNIVERSITY  OF  FREIBURG. 


FIRST    AMERICAN  EDITION, 

REVISED  AND   ILLUSTRATED  WITH  538  ENGRAVINGS  ON  WOOD,  AND  TWO  COLORED  PLATES. 


PHILADELPHIA: 
LEA    AND    BLANCHARD. 

1848. 


Entered  according  to  the  Act  of  Congress,  in  the  year  184S,  by 

LEA  AND  BLANCHARD, 
in  the  Clerk's  Office  of  the  District  Court  for  the  Eastern  District  of  Pennsylvania. 


PHILADELPHIA : 
T.  if.  AND  P.  G.  COLLINS,  PRINTERS. 


PUBLISHERS'  ADVERTISEMENT. 


THE  Treatise  on  Physics,  by  Professor  Miiller,  now  presented 
to  the  American  public,  is  the  first  of  a  series  of  works  on  the 
different  branches  of  science,  now  passing  through  the  press  of 
Bailliere  in  London ;  and  which,  from  its  thorough  character  and 
extended  range,  is  much  needed  in  this  country.  In  preparing 
it,  the  American  publishers  have  availed  themselves  of  the  ser- 
vices of  a  competent  editor,  who  has  made  various  alterations 
and  additions.  Among  the  changes  considered  necessary,  the 
principal  is  the  introduction  of  the  English  standard  of  weights 
and  measures,  in  addition  to  the  Continental  system  adopted  by 
the  author.  Articles  have  also  been  added,  on  the  electro-mag- 
netic telegraph,  electrotype,  steam  engine,  &c.,  with  the  necessary- 
illustrations,  while  various  errors  of  importance,  which  had  escaped 
the  London  editor,  have  been  corrected. 

The  publishers  hope  that  the  care  exercised  in  the  revision  of 
the  work,  and  the  accuracy  of  the  text,  which  it  has  been  their 
aim  to  secure,  will  be  deemed  of  sufficient  importance  to  enhance 
the  value  of  a  work  which  has  already  received  deservedly  high 
commendation. 

PHILADELPHIA,  January r,  1848. 


i* 
4203.-J 


PREFACE. 


IN  laying  the  following  pages  before  the  Public,  it  seems 
necessary  to  state  that  the  design  of  them  is  to  render  more  easily 
accessible,  a  greater  degree  of  knowledge  of  the  general  princi- 
ples of  Physics  and  Meteorology,  than  is  usually  to  be  obtained, 
without  the  sacrifice  of  a  greater  amount  of  time  and  labor  than 
most  persons  can  afford,  or  are  willing  to  make.  The  subjects 
of  which  this  volume  treats,  are  very  numerous — more  numerous, 
in  fact,  than  at  first  sight  it  would  seem  possible  to  embrace  in 
so  small  a  compass.  The  Author  has,  however,  by  a  system  of 
most  judicious  selection  and  condensation,  been  enabled  to  intro- 
duce all  the  most  important  facts  and  theories  relating  to  Statics, 
Hydrostatics,  Dynamics,  Hydrodynamics,  Pneumatics,  the  Laws 
of  the  Motions  of  Waves  in  general,  Sound,  the  Theory  of  Musical 
Notes,  the  Voice  and  Hearing,  Geometrical  and  Physical  Optics, 
Magnetism,  Electricity  and  Galvanism,  in  all  their  subdivisions, 
Heat,  and  Meteorology,  within  the  space  of  an  ordinary  middle- 
sized  volume.  Of  the  manner  in  which  the  translator  has 
executed  his  task,  it  behoves  him  to  say  nothing;  he  has 
attempted  nothing  more  than  a  plain,  and  nearly  literal  version 
of  the  original.  He  cannot,  however,  conclude  this  brief  intro- 
ductory note,  without  directing  the  attention  of  his  readers  to 
the  splendid  manner  in  which  the  publisher  has  illustrated  this 
volume. 

E.  C.  0. 

LONDON, 
AUGUST,  1847. 


TABLE    OF    CONTENTS. 


PAGE 

INTRODUCTION      .  .  ...  25 


SECTION    I. 

GENERAL  PROPERTIES  OF  BODIES  .  .  29 


SECTION    II. 

EQUILIBRIUM      OF      FORCES. 

CHAPTER  I. 

Equilibrium  and  decomposition  of  forces  in  the  so  called  simple  machines  43 

CHAPTER  II. 
Molecular  equilibrium      .......  72 

CHAPTER  HI. 

Hydrostatics;  or  the  theory  of  the  equilibrium  of  liquids  .  .  76 

CHAPTER  IV. 

Molecular  actions  between  solid  and  liquid  bodies,  and  between  the  sepa- 
rate particles  of  liquids      ......  108 

CHAPTER   V. 

Of  the  equilibrium  of  gases,  and  of  atmospheric  pressure  .  .  116 

CHAPTER  VI. 

Attraction  between  gaseous  and  solid,  as  well  as  between  gaseous  and 

liquid  bodies  ....  145 


X  CONTENTS. 

SECTION    III. 

OF   MOTION    AND    ACCELERATING    FORCES. 

CHAPTER  I. 

PAGE 

Different  kinds  of  motion  .  .  .  .  .  .  148 

CHAPTER  II. 
Laws  of  the  motion  of  liquids  .  .  .  .  .  .  179 

CHAPTER  III. 
Motion  of  gases  ........  197 


SECTION    IV. 

ACOUSTICS. 

CHAPTER   I. 

Laws  of  the  motion  of  waves  in  general,  and  especially  of  waves  of 

sound          ........  207 

CHAPTER  II. 
Laws  of  the  vibrations  of  musical  tones  ....  227 

CHAPTER   III. 
Of  the  voice  and  hearing  ......  246 


SECTION    V. 

INTRODUCTION  OF  LIGHT  ......  252 

CHAPTER   I. 
Reflection  of  light  .......  258 

CHAPTER   II. 
Dioptrics   .........  270 

CHAPTER  III. 
Decomposition  of  white  light       ......  285 


CONTENTS.  xi 

CHAPTER   IV. 

PAGE 

Of  the  eye  and  optical  instruments  .  .  .  296 

CHAPTER   V. 
Phenomena  of  interference          .....  326 

CHAPTER  VI. 
Chemical  actions  of  light  ....  343 


SECTION    VI. 

MAGNETISM  AND  ELECTRICITY. 

PART    I. MAGNETISM. 

CHAPTER    I. 

Mutual  action  of  magnets  on  each  other  and  on  magnetic  bodies  .  347 

CHAPTER   II. 
Of  the  magnetic  actions  of  the  earth        ....  354 

PART    II. ELECTRICITY. 

CHAPTER   I. 
Of  electric  actions  .  .  .  .  .  .  368 

CHAPTER  II. 
Electricity  by  induction     .......  375 

CHAPTER  III. 
Of  electrical  forces  .......  387 

CHAPTER.  IV. 
Of  combined  electricities  ......  390 

CHAPTER  V. 

Of  electric  light,  and  the  motions  of  electrified  bodies     .  .  .  397 

PART  III. GALVANISM. 

CHAPTER  I. 

On  the  electricity  of  contact,  and  on  the  galvanic  circuit  .  .  402 

CHAPTER  II. 

Actions  of  the  galvanic  current    .  .  .  .  .  .  419 


Xii  CONTENTS. 

PART  IV. ELECTRO-MAGNETISM. 

CHAPTER  I. 

Magnetic  actions  of  the  current   . 

CHAPTER  II. 
Phenomena  of  induction  .  ... 

PART  V. 

Thermo-electric  currents  and  animal  electricity   . 


SECTION    VII. 

OF  HEAT. 
CHAPTER  I. 
Expansion  ..... 

CHAPTER  II. 

Change  of  state  of  aggregation    . 

CHAPTER  III. 
Specific  heat  of  bodies      .... 

CHAPTER  IV. 

Transmission  of  heat       .... 

CHAPTER  V. 

Different  sources  of  heat 


SECTION    VIII. 

METEO  ROZOGT. 

CHAPTER  I. 

Distribution  of  heat  on  the  earth's  surface  ....  555 

CHAPTER  II. 
Of  the  pressure  of  the  atmosphere  and  of  the  winds       .  .  .  578 

CHAPTER  III. 
Of  atmospheric  moisture  .  .  .  .  .  .  589 

CHAPTER  IV. 
Optical  phenomena  of  the  atmosphere     .....  606 

CHAPTER  V. 
On  atmospheric  electricity  .....  616 


PRINCIPLES 


OF 


PHYSICS    AND    METEOROLOGY. 


INTRODUCTION. 

General  Idea. — The  grand  spectacle  that  is  ever  present  to  our 
eyes  in  the  vast  realm  of  nature  excites  within  us  so  ardent  a  thirst 
for  knowledge,  that  we  feel  ourselves  irresistibly  impelled  to  the 
consideration  of  the  combined  causes  that  have  produced  these 
wondrous  results.  Such  subjects  fall  within  the  department  of 
natural  philosophy,  whose  task  it  is  to  trace  the  connecting  link 
between  the  different  phenomena  of  nature,  and,  as  far  as  this  is 
possible,  to  unravel  the  causes  from  which  they  have  originated. 

The  combined  natural  sciences  treat  of  bodies — a  word  which 
we  must  not  receive  in  the  limited  sense  in  which  it  is  under- 
stood by  the  mathematician,  who  looks  only  to  the  relations  of 
space,  disregarding  the  matter  that  fills  space ;  while  it  is  to  the 
properties  of  this  very  matter  that  the  natural  philosopher  devotes 
his  especial  attention.  The  interior  of  bodies  is  closed  to  our  view, 
their  external  appearance  being  only  made  known  to  us  by  means 
of  what  we  learn  concerning  them  through  our  senses.  Thus, 
a  body,  standing  in  no  connection  with  our  senses,  has,  so  far  as 
we  are  concerned,  no  existence ;  and  it  is  probable  that  there  is 
still  much  passing  around  us  in  nature  of  which  we  have  no  con- 
ception, from  the  want  of  some  additional  sense  by  which  we  can 
recognize  its  existence. 

The  province  of  the  natural  sciences  is,  therefore,  to  trace  the 
connection  existing  between  the  phenomena  brought  within  the 
scope  of  our  knowledge  by  means  of  the  senses,  and  so  to  arrange 
3 


26  INTRODUCTION. 

them,  that  they  may  elucidate  each  other,  and  manifest  the  mu- 
tual dependence  existing  between  them.  If  we  are  able  to  trace 
a  phenomenon  in  its  connection  with  other  phenomena,  we  have 
explained  it;  and  a  natural  law  is  obtained  as  soon  as  the 
unchangeable  link  of  connection  existing  between  the  natural 
phenomena  is  understood,  even  should  we  still  remain  ignorant  of 
the  final  cause. 

Division. — The  vast  department  of  the  natural  sciences  divides 
itself  into  two  great  branches — Natural  History  and  Natural 
Philosophy.  The  former  teaches  us  to  know  the  nature  of  indi- 
vidual objects,  and  arranges  them  in  systems  according  to  their 
different  characters;  while  the  latter  endeavors  to  lay  open  the 
natural  laws  of  the  material  world. 

By  the  term  physics,  we  understand  that  branch  of  the  natural 
sciences  which  treats  of  phenomena  which  do  not  depend  upon  a 
change  of  the  constitution  of  bodies ;  the  latter  falling  under  the 
head  of  chemistry. 

As  may  be  readily  conceived,  it  is  not  always  easy  to  trace  with 
accuracy  the  line  of  demarcation  between  these  two  sciences. 
They  are  most  intimately  connected  with  each  other,  in  some 
measure  even  forming  one  whole,  which  appears  to  have  been 
divided  chiefly  owing  to  its  embracing  so  wide  and  increasing  a 
field  of  observation. 

Method. — We  must  now  point  out  the  manner  in  which  the 
student  may  attain  to  a  knowledge  of  the  laws  of  nature,  and  by 
what  means  the  facts  already  ascertained  have  been  acquired.  The 
sources  of  knowledge,  as  well  as  the  methods  of  acquiring  it,  are 
not  and  cannot  be  the  same  for  all  sciences.  The  mathematician 
may,  starting  from  his  own  self-acquired  conceptions,  develop  his 
science  wholly  out  of  himself;  and  we  might  even  conceive  the 
possibility  of  a  man  shut  up  within  four  walls,  and  separated  from 
all  communication  with  the  outer  world,  constructing  the  whole 
science  of  mathematics  from  his  own  ideas  of  space  and  number.* 

*  [We  find  the  same  idea  expressed  in  nearly  the  same  words  in  Herschel's 
beautiful  Essay  "  On  the  Study  of  Natural  Philosophy :" — "  A  clever  man,  shut  up 
alone,  and  allowed  unlimited  time,  might  reason  out  for  himself  all  the  truths  of 
mathematics  by  proceeding  from  those  simple  notions  of  space  and  number,  of 
which  he  cannot  divest  himself  without  ceasing  to  think.  But  he  could  never  tell 
by  any  effort  of  reasoning  what  would  become  of  a  lump  of  sugar  if  immersed  in 
water,  or  what  impression  would  be  produced  on  his  eye  by  mixing  the  colors  yel- 
low and  blue."  P.  76.] 


INTRODUCTION.  27 

Seen  from  this  point  of  view,  mathematics  is  a  purely  speculative 
science,  the  very  reverse  of  natural  philosophy,  which  treats  of 
objects  that  solely  and  alone  come  to  our  knowledge  through  the 
perceptions  of  sense  and  in  the  course  of  experience. 

The  ancients  were  wholly  unacquainted  with  any  science  of 
natural  investigation  that  was  based  upon  experience ;  and  hence 
their  philosophical  speculations  upon  the  world  in  general,  and 
upon  the  rise  and  origin  of  all  material  objects,  are  nothing  but 
confused  conjectures,  and  possessed  of  little  value ;  frequently, 
indeed,  standing  in  direct  opposition  to  fact  and  experience. 

Even  in  the  middle  ages  the  natural  sciences  were  not  much 
more  developed,  partly  because  the  human  mind  was  directed  in 
other  channels,  and  partly  because  the  Aristotelian  philosophy  was 
held  in  such  high  esteem  that  all  inquiries  and  progress  were  alike 
checked. 

Galileo  was  the  first  to  enter  the  path  of  practical  experiment, 
and  Bacon  showed  that  there  was  no  other  road  that  would  lead 
to  a  knowledge  of  the  laws  of  nature. 

The  only  source  from  whence  we  can  draw  our  knowledge  of 
nature  is  the  perception  of  the  senses, — practical  experience, — 
observation.  Hence  we  derive  the  materials  which  must  be  united 
and  worked  into  a  science  by  our  mental  activity. 

We  derive  our  scientific  perceptions  either  from  changes  effected 
by  nature  itself,  or  we  designedly  place  bodies  in  those  conditions 
that  may  call  forth  certain  phenomena.  In  the  first  case  we  make 
observations;  in  the  second,  experiments. 

By  means  of  good  observations,  and  judiciously-conducted 
experiments,  we  learn  to  know  the  external  connection  of  the 
phenomena  of  nature.  And  this  connection  is  what  we  term  a 
natural  law. 

By  the  aid  of  experiments  we  may  arrive  at  a  knowledge  of 
these  laws,  even  while  we  remain  wrholly  unacquainted  with  their 
internal  connection,  and  with  the  nature  of  forces. 

The  law  of  the  refraction  of  light  was  known  long  before  any 
correct  idea  was  formed  as  to  the  nature  of  light ;  and,  in  the 
present  day,  we  know  the  laws  of  the  distribution  of  electricity, 
but  we  have  little  or  no  knowledge  concerning  the  nature  of 
electricity  itself. 

It  is  only  the  external  connection  of  things  that  can  be  discovered 
by  perception ;  and  we  can  hazard  nothing  more  than  hypotheses 


28  INTRODUCTION. 

as  to  the  internal  causes  of  phenomena,  or  the  origin  of  the  forces 
from  which  they  are  educed.  These  hypotheses  are  like  questions 
which  we  put  to  Nature,  but  the  answers  she  gives  are  not  simply 
"yes"  and  "no;"  but  it  can  be  so,  or  it  cannot.  Nevertheless, 
from  these  hypotheses  deductions  may  generally  be  drawn,  which 
can  subsequently  be  confirmed  or  refuted  by  further  observations. 
In  proportion  to  the  number  of  facts  that  can  be  explained  by 
help  of  an  hypothesis,  and  the  more  we  can  confirm  it  by  new 
observations,  the  greater  probability  does  it  acquire. 

In  all  branches  of  physics  we  shall  find  examples  of,  and  evi- 
dence favoring  the  correctness  of  these  views. 


SECTION   I. 


GENERAL    PROPERTIES    OF    BODIES. 

As  PHYSICS  treats  of  bodies,  it  is  most  essential  to  form  to 
one's  self  a  representation  of  the  nature  of  these  bodies,  and  this 
object  is  the  most  readily  attained  by  the  consideration  of  those 
general  properties  which  we  observe  to  exist  in  all  bodies,  what- 
ever other  differences  they  may  manifest. 

Thus,  it  is  essential  to  the  existence  of  a  body  that  it  occupy  a 
limited  space,  possess  the  property  of  extension,  and  that  no  other 
body  occupy  the  same  space  at  the  same  time;  this  latter  con- 
dition indicating  the  property  of  impenetrability.  Besides  these 
two  properties,  without  which  we  can  form  no  conception  of  mat- 
ter, we  observe  other  general  properties,  as  divisibility,  extensi- 
bility, compressibility,  porosity,  inertia,  and  gravity. 

Divisibility. — As  far  as  our  experience  goes,  we  find  that  all 
bodies  are  divisible ;  that  is,  they  may  be  divided  into  smaller 
and  still  smaller  particles.  Here  the  question  arises : — What  are 
the  limits  of  this  divisibility  ?  And  again  : — Do  we  by  continued 
reduction  arrive  at  particles  which,  although  still  perceptible  to. 
the  senses,  are  incapable  of  being  further  divided?  Experience 
furnishes  us  with  the  reply,  that  divisibility  continually  oversteps 
the  limits  of  sensible  perception.  As  an  instance  of  extreme 
divisibility  we  may  adduce  musk,  which  will  continue  year  after 
year  to  fill  an  apartment  with  the  most  intensely-penetrating  odor, 
without  any  perceptible  loss  of  weight. 

Chemically,  compound  bodies  afford  the  best  evidence  that 
divisibility  passes  the  limits  of  sensible  perception.  In  cinnabar, 
for  example,  which  is  composed  of  mercury  and  sulphur,  and  may 
easily  be  separated  into  these  constituents,  we  are  unable  to 
distinguish  small  particles  of  sulphur  and  mercury  from  one 
another;  even  under  the  best  microscope  it  appears  to  be  a  per- 
fectly homogeneous  mass. 

3* 


30  PROPERTIES  OF  BODIES. 

But,  although  divisibility  extends  far  beyond  the  limits  per- 
ceptible to  sense,  it  must  not  be  assumed  that  it  is  wholly 
unlimited ;  for  to  adopt  such  art  assumption  were,  in  other  words, 
to  admit  that  the  size  of  the  ultimate  undivisible  particle  is  null, 
while  it  is  evident  that,  if  the  ultimate  particle  have  no  extension, 
it  cannot  enter  into  the  composition  of  an  extended  body. 

It  is  upon  these  considerations  that  the  natural  philosopher 
bases  the  hypothesis  that  all  bodies  are  composed  of  minute  par- 
ticles, which  cannot  be  further  disintegrated,  but  are  indivisible, 
and  therefore  termed  atoms. 

This  fundamental  view  of  the  constitution  of  bodies  is  now 
universally  embraced  by  the  natural  philosopher,  and  the  chemist, 
as  the  atomic  theory. 

In  speaking  of  small  particles,  without  actually  wishing  to 
designate  them  as  ultimate  portions  or  atoms,  we  generally  make 
use  of  the  term  molecules,  which  is  synonymous  with  particles 
of  a  mass. 

Extensibility  and  Compressibility. — A  second  general  property 
is  extensibility,  on  which  depends  compressibility.  The  same 
body  does  not  always  possess  a  similar  volume,  since  it  may  be 
diminished  by  pressure  and  cold,  and  enlarged  by  expansion  and 
heat.  If,  then,  we  assume  that  the  atoms  are  invariably  the 
same,  we  can  only  explain  extensibility  on  the  hypothesis  that 
the  atoms  are  not  in  immediate  contiguity  with  each  other,  but 
are  separated  by  interstices,  according  to  the  enlargement  or 
diminution  of  which  the  volume  of  the  body  changes. 

Porosity. — The  interstices  which  occur  between  the  different 
particles  of  bodies  are  named  pores ;  and,  if  we  apply  the  same 
term  to  the  interstices  between  the  atoms  of  bodies,  it  is  evident, 
from  what  has  been  already  stated,  that  everybody  is  porous,  and 
that  porosity  is  therefore  a  general  property.  In  common  speech, 
however,  we  understand  by  the  term  pore  an  interstice  sufficiently 
large  to  admit  of  the  passage  of  fluids  and  gases;  and,  according 
to  this  definition,  porosity  is  certainly  not  a  general  property.  A 
sponge,  all  artificial  textures — chalk,  pumice,  &c. — are  porous  in 
the  restricted  sense  of  the  word. 

Different  Nature  of  Atoms. — After  developing  the  fundamental 
idea  of  the  atomic  theory  by  the  consideration  of  divisibility  and 
extensibility,  we  will  pass  to  the  observation  of  the  mode  in  which 
different  bodies  are  formed  from  atoms,  and  next  consider  the 
remaining  common  properties  of  matter. 


ARRANGEMENT  OF  ATOMS.  31 

We.  find  that  there  are  in  nature  a  number  of  bodies,  the  pro- 
perties of  which  are  so  different  that  we  must  necessarily  assume 
that  the  atoms  of  which  they  are  composed  likewise  differ  in  their 
nature.  If,  for  instance,  we  consider  sulphur  and  lead,  we  find 
that  the  relations  of  these  two  bodies  are  remarkably  different,  a 
fact  which  can  only  be  explained  by  the  hypothesis  that  the  atoms 
of  sulphur  are  not  of  the  same  nature  as  those  of  lead. 

Most  bodies  are  not  composed  of  homogeneous  parts,  but  of 
such  as  differ  among  themselves,  even  where  they  appear  to  be  of 
like  nature,  as  we  mentioned  in  the  case  of  cinnabar,  which  is 
composed  of  sulphur  and  mercury ;  and  as  in  water,  which  we 
find  to  be  a  compound  of  oxygen  and  hydrogen ;  and  in  common 
salt,  which  is  composed  of  chlorine  and  sodium.  Bodies  such  as 
these  are  said  to  be  chemical  compounds,  in  contradistinction  to 
those  which  are  not  capable  of  being  decomposed  into  different 
constituents,  and  which  are,  therefore,  called  simple  bodies,  or 
elements.  There  are  fifty-five  or  six  of  such  simple  bodies  or 
elements,  which  hitherto  at  least  have  not  been  found  to  admit  of 
further  decomposition.  The  consideration  of  these  elements,  and 
of  the  mode  in  which  they  enter  into  the  composition  of  other 
bodies,  falls  within  the  province  of  chemistry. 

Aggregate  Conditions. — In  addition  to  the  above  differences  of 
bodies,  we  observe  others,  which  depend,  not  upon  a  difference 
in  their  constituent  parts,  but  upon  the  manner  in  which  the 
particles  are  united.  Thus  one  and  the  same  substance  may 
assume  totally  different  forms,  as  water,  which  is  solid  when  it 
appears  as  ice,  fluid  as  water,  and  gaseous  as  steam.  Without 
changing  its  composition,  we  may  convert  water  into  ice,  and  ice 
into  water — vaporize  wrater,  and  again  condense  it. 

All  bodies  with  which  we  are  acquainted  are  in  one  of  these 
three  conditions,  either  solid,  fluid,  or  gaseous  (aeriform). 

Solid  bodies  have,  independently  of  the  slight  changes  effected 
on  them  by  heat,  a  constant  volume  and  an  independent  form; 
and  it  requires  a  greater  or  less  amount  of  force  to  divide  a  solid 
body.  Thus  it  is  impossible  to  compress  a  piece  of  iron  to  the 
half  or  the  third  of  its  volume,  or  make  it  fill  a  space  twice  or 
three  times  as  great  as  it  occupies,  it  being  only  by  extreme  force 
that  we  are  enabled  to  change  its  form  or  to  divide  it. 

Fluids  have,  in  the  same  sense  as  solid  bodies,  a  constant 
volume ;  that  is,  although  they  may  be  slightly  compressed  by 


32  PROPERTIES  OF  BODIES. 

strong  pressure,  or  somewhat  expanded  by  the  action  of  heat,  the 
change  of  volume  thus  induced  is  very  inconsiderable.  We  cannot 
compress  the  water  which  fills  a  quart  bottle  into  a  vessel  of  half 
the  size,  and,  if  we  pour  the  fluid  into  one  of  twice  the  bulk,  the 
vessel  will  only  be  half  filled.  But  fluids  differ  from  solid  bodies 
in  having  no  independent  form,  the. figure  they  assume  being  that 
of  the  vessel  containing  them,  the  surrounding  solid  body,  while 
the  liquid  presents  a  horizontal  surface  where  it  intersects  the 
sides  of  the  vessel.  Fluids  also  differ  essentially  from  solid  bodies 
in  the  least  imaginable  force  being  sufficient  to  separate  their 
particles. 

Gaseous  bodies  have  neither  an  independent  form  nor  a  definite 
volume;  the  space  which  they  occupy  dependingonly  upon  external 
pressure.  A  volume  of  air  may  easily  be  reduced  to  the  half,  the 
fourth,  or  even  the  tenth  of  its  original  bulk;  and,  conversely,  we 
find  that,  on  admitting  the  same  volume  of  air  into  a  vacuum 
twice,  four  times,  or  ten  times  as  large,  the  air  will  completely  fill 
it,  thus  proving  that  gaseous  bodies  have  a  tendency  to  expand  as 
far  as  possible.  Easy  divisibility  is  alike  common  to  gases  and 
fluids. 

The  external  differences  must,  according  to  our  views  of  the 
composition  of  bodies,  depend  upon  the  circumstance  that  in  solid 
bodies  the  individual  particles  remain  at  certain  distances  from, 
and  in  fixed  relative  positions  to,  each  other ;  in  fluids  they  remain 
at  fixed  distances,  but  may  easily  be  displaced ;  while  in  gaseous 
bodies  the  component  parts  show  a  constant  tendency  to  separate. 

Molecular  Forces. — As  a  force  is  necessary  to  separate  the 
particles  of  a  solid  body,  and  as  also  an  external  force  is  necessary 
to  hold  together  the  particles  of  a  gaseous  body,  it  is  clear  that 
bodies  cannot  be  formed  by  means  of  a  simple  juxtaposition  of 
their  atoms,  since  they  would  then  be  nothing  more  than  an  un- 
connected mass  somewhat  in  the  condition  of  a  sand  heap.  There 
must,  consequently,  be  forces  which  hold  together  the  particles  of 
a  solid  body  in  their  relative  position,  imparting  to  them  a  fixed 
internal  structure  and  external  form;  and  in  like  manner  there 
must  be  forces  which  act  repulsively  amongstthe  particles  of  a  gas. 
These  forces,  which  are  continuously  acting  between  the  adjacent 
molecules  of  bodies,  are  termed  molecular  forces.  The  force 
which  holds  together  the  particles  of  a  solid  body  is  termed  the 
force  of  cohesion,  which  we  assume  to  be  called  forth  by  a  mutual 


INERTIA.  33 

attraction  of  the  atoms.  Now,  if  atoms  mutually  attract  each 
other,  it  is  not  easy  to  understand  how  these  can  also  mutually 
repel  each  other,  and,  therefore,  in  order  to  explain  this  repulsion 
observed  in  gases,  we  assume  that  there  is  another  and  an  op- 
posite force,  which  we  term  the  force  of  expansion. 

Solid  bodies  may  be  melted  by  heat ;  that  is,  they  may  be 
transformed  into  a  fluid  condition ;  and  through  the  same  agency 
fluids  may  be  reduced  to  the  state  of  vapor ;  it  follows,  therefore, 
that  heat  is  opposed  to  the  force  of  cohesion,  and  hence  we  may 
assume  it  to  be  identical  with  the  force  of  expansion.  Let  us 
suppose  the  molecules  of  a  body  to  be  surrounded  by  an  atmo- 
sphere of  heat  which  modifies  the  attraction  of  the  molecules,  and 
we  shall  then  understand  how  the  attractive  and  the  repulsive 
forces  proceed  from  one  common  centre.  The  preponderance  of 
the  expansive  or  of  the  repulsive  force  will  determine  whether  a 
body  be  solid  or  gaseous,  while  an  equilibrium  of  both  forces  cha- 
racterizes a  fluid. 

Inertia. — Throughout  the  whole  kingdom  of  nature  no  change 
in  the  condition  of  things  can  occur  without  a  special  cause. 
Thus  whatever  change  may  occur  in  a  body,  wrhether  it  be  relat- 
ing to  rest  or  to  motion,  or  to  a  change  in  its  aggregate  condition, 
must  be  occasioned  by  some  force.  If  a  body  be  at  rest,  a  force 
is  necessary  to  put  it  into  motion,  and,  conversely,  it  cannot  be 
reduced  to  a  state  of  rest  from  motion  without  the  agency  of  some 
force,  for  a  body  once  put  into  motion,  will  continue  that  motion 
with  unchanging  velocity,  in  an  unchanging  direction,  until  its 
course  be  arrested  by  external  impediments.  This  property  of  a 
body  we  term  inertia. 

We  find  numerous  examples  in  every-day  life  elucidating  this 
law  of  inertia.  Thus  the  wheel  of  an  engine  continues  to  pursue 
its  course  after  the  force  which  impelled  it  has  been  arrested,  and 
it  would  continue  to  run  on  for  ever  if  the  motion  were  not 
constantly  impeded  by  friction. 

In  running  fast  the  speed  cannot  suddenly  be  checked.  A  man 
standing  upright  in  a  boat  will  fall  backwards  when  the  boat  is 
pushed  from  the  shore,  and  will  be  urged  forward  as  the  boat 
touches  the  land.  We  shall  subsequently  have  frequent  opportu- 
nities of  alluding  to  the  influence  of  the  law  of  inertia  upon  many 
phenomena  of  motion.  According  to  the  law  of  inertia  a  body 
must  exercise  a  resistance  against  every  force  which  removes  it 
from  a  condition  of  rest  to  one  of  motion;  or  which  hastens, 


34  PROPERTIES  OF  BODIES. 

impedes,  or  tries  wholly  to  arrest  it  when  in  motion.  It  is, 
therefore,  clear,  that  the  action  exercised  upon  the  condition  of 
motion  of  a  body  must  depend  on  the  one  hand  upon  the  intensity 
of  the  force,  and  on  the  other  upon  the  degree  of  inertia  in  the 
body. 

The  larger  the  quantity  of  matter — that  is  to  say,  the  greater 
the  mass  is  on  which  a  force  acts — so  much  the  greater  will  be  the 
resistance  it  offers;  and  we  judge  of  the  mass  of  a  body  by  the 
amount  of  resistance  which  it  can  oppose  by  its  inertia  to  an 
accelerating  or  retarding  force.  This  idea  of  inertia  and  mass 
cannot  be  rendered  very  clear  until  we  have  occupied  ourselves 
somewhat  with  the  study  of  the  laws  of  gravity  and  motion. 

Gravity. — If  we  remove  a  piece  of  stone  or  wood  from  the 
ground  and  throw  it  from  our  hands,  it  will,  when  left  to  itself, 
fall  until  it  reaches  the  earth,  or  meets  with  any  object  to  arrest 
its  course.  As  matter  is  inert,  it  cannot  of  itself  pass  from  a 
state  of  rest  into  one  of  motion.  If,  then,  we  see  that  a  body  at 
rest  begins  to  move  at  the  same  moment  that  we  deprive  it  of  its 
support,  we  must  ascribe  this  to  a  force,  and  to  this  force  we 
apply  the  term  gravity. 

Gravity  is,  therefore,  the  force  which  compels  bodies  to  fall. 
We  must  not,  however,  suppose  that  its  power  is  limited  to  this 
action,  for  we  shall  soon  see  that  gravity  produces  other  pheno- 
nomena,  and  other  motions.  The  direction  of  rivers  which  flow 
into  the  sea,  the  rising  of  a  piece  of  cork  from  the  bottom  of  the 
water  to  the  surface,  the  ascent  of  the  air-balloon,  are  all  the 
effects  of  this  force. 

There  is  no  better  means  of  ascertaining  the  direction  of  the 
force  of   gravity  than  the   following: — Fasten  a   string  at  one 
extremity,  and  attach  a  small  heavy  weight  at  its  other  extremity; 
the  direction  of  the  thread,  when  it  is  tense  and  at  rest,  will 
j  determine  with  accuracy  the  direction  of  gravity.  This  little 
'  instrument  is  called  a  plummet,  and  the  line  which  the  thread 
/     forms  in  a  state  of  equilibrium  is  the  vertical.     The  direc- 
tion of  gravitation  is  therefore  identical  with  that  of  the 
plummet,  and  nothing  can  be  easier  than  at  all  times,  and  in 
all  places,  to  ascertain  this  direction  of  gravitation.    As  we 
shall  see  when  we  treat  of  hydrostatics,  the  upper  surface  of 
every  fluid  at  rest  must  be  at  right  angles  with  the  direction 
of  gravitation,  or  we  may  express  the  same  thing  differently 


FORCE  OF  GRAVITY.  35 

by  saying  that  the  direction  of  gravitation  is  always  at  right  angles 
with  the  earth's  surface.  Here,  as  may  easily  be  supposed,  we  do 
not  speak  of  the  true  surface  of  the  earth  with  its  hills  and  valleys, 
but  of  an  ideal  surface,  of  which  we  must  form  a  conception  in  the 
following  manner: — If  we  assume  that  the  Atlantic  Ocean,  the 
South  Sea,  and  all  other  seas,  were  for  a  moment  perfectly  at  rest, 
then  their  vast  superficies  would  form  a  part  of  a  spherical  sur- 
face; and  if,  further,  we  assume  that  the  different  parts  of  this 
surface  wrere  spread  under  the  surface  of  the  land,  still  retaining 
their  curvature,  they  would  form  a  spherical  surface  without  hills 
or  valleys.  This  partly  imaginary  and  partly  actual  surface  is 
what  we  term  the  level  of  the  sea — the  horizontal  line.  When, 
therefore,  we  say  that  Mount  Blanc  is  14,690  feet  above  the  level 
of  the  sea,  we  mean  that  a  perpendicular  dropped  from  the  sum- 
mit of  the  mountain  must  measure  14,690  feet  in  order  to  reach 
this  ideal  surface.  In  Holland  there  are  whole  districts  below 
the  surface  of  the  sea;  that  is  to  say,  this  imaginary  level  is  at  an 
elevation  above  the  heads  of  the  inhabitants. 

The  force  of  gravity  is  always  directed  towards  the  central 
point  of  the  earth,  as  we  perceive  from  what  has  been  already 
stated.  The  directions  of  the  plummet  at  two  different  parts  of 
the  earth  are,  consequently,  not  parallel,  for  they  make  a  certain 
angle  with  each  other,  the  point  of  which  coincides  with  the  cen- 
tral point  of  the  earth.  Berlin  and  the  Cape  of  Good  Hope  are 
two  places  lying  in  nearly  the  same  meridian  line.  Berlin  is  52° 
31'  13"  north  of  the  equator,  and  the  Cape  of  Good  Hope  33°  55' 
15"  south  of  the  same  line;  and  if  we  draw  two  lines  towards 
the  central  point  of  the  earth,  the  one  from  Berlin  and  the  other 
from  the  Cape,  we  find  that  they  make  an  angle  of  86°  26'  28'', 
being  the  angle  which  the  plummet  at  Berlin  makes  with  the 
plummet  at  the  Cape.  If  the  experiments  be  made  at  two  points 
lying  within  the  circumscribed  space  of  an  apartment,  or  even  at 
the  extreme  ends  of  a  city,  no  deviation  in  the  direction  of  the 
plummet  will  be  perceived;  the-  reason  of  which  is,  that  the 
central  point  of  the  earth  (the  focus  towards  which  the  two  lines 
incline)  is  distant  from  the  surface  of  the  earth  more  than  six 
millions  of  metres*  (3960  miles)  (the  radius  of  the  earth).  Now, 
as  200  metres  (218,72  yards)  scarcely  compose  the  30,000th  part 


*  The  metre  is  equal  to  39.37  English  inches. — Tn. 


36  PROPERTIES  OF  BODIES. 

of  the  earth's  radius,  it  follows  that  two  plummets  placed  at  the 
distance  of  200  metres  from  each  other  would  form  an  angle  of 
about  6.3  seconds.  If  the  places  at  which  the  experiment  is 
attempted  were  less  removed  from  each  other  the  angle  would 
cease  to  be  appreciable. 

If  a  body  be  impeded  in  its  fall  by  the  intervention  of  some 
other  supporting  body,  the  action  of  the  force  of  gravity  does 
not  cease,  but  manifests  itself  in  this  case  by  pressure  upon  the 
intervening  object. 

Gravity  is  a  general  property  of  bodies ;  that  is,  it  is  common 
to  fluids  and  gases,  as  well  as  to  solid  bodies.  The  falling  of  the 
rain  drop  proves  the  gravity  of  fluids,  and  we  shall  subsequently 
adduce  instances  of  the  gravity  possessed  by  gaseous  bodies,  and 
consequently  show  that  the  whole  atmosphere  surrounding  our 
globe  presses  upon  the  earth's  surface. 

Weight. — The  amount  of  pressure  exercised  by  a  body  upon 
another  body  upon  which  it  rests  is  called  its  weight;  this  pres- 
sure increases  with  the  number  of  material  particles  of  the  body. 
In  order  to  compare  the  weight  of  different  bodies,  we  make  use 
of  the  balance,  the  application  of  which  is  familiar  to  all,  and  its 
arrangement  we  shall  describe  subsequently. 

In  France  the  gramme  is  the  legal  unit  of  weight,  and  at  the 
present  day  it  is  received  almost  universally  as  the  unit  measure 
in  scientific  researches.  The  gramme  is  the  weight  of  a  cubic 
centimetre  of  pure  water  in  its  state  of  greatest  density.  The 
French  system  of  weights  has  this  great  advantage  over  others, 
that  the  units  of  weight  and  measure  stand  in  a  simple  relation  to 
each  other,  so  that  it  is  easy  to  judge  of  the  weight  of  a  body  by 
its  size,  and  vice  versa.* 


*  A  measure  can  only  be  considered  as  unalterably  fixed  when  it  has  been  de- 
rived from  some  undeviating  size  or  space  in  nature,  as  is  the  case  with  the  French 
system  of  measures.  Thus  any  certainty  other  systems  now  possess  has  been 
derived  from  a  comparison  with  the  system  established  in  France. 

The  undeviating  length  which  has  become  the  standard  for  this  system  is  the 
earth's  meridian — that  is,  the  circumference  of  a  large  circle  of  the  globe,  passing 
through  both  poles.  The  forty  millionth  part  of  this  line  is  a  metre. 

The  length  of  a  meridian  of  the  earth  was  ascertained  by  a  series  of  the  most 
carefully  conducted  measurements,  and  for  this  purpose  the  old  French  unit  of 
measure — the  toise — was  used  for  a  basis ;  it  was  in  this  way  accurately  deter- 
mined how  many  of  these  toises  were  contained  in  the  earth's  meridian,  and  con- 
sequently what  was  the  exact  length  of  the  toise.  As,  however,  it  was  resolved 
that  an  entirely  new  system  of  measures  should  be  established,  the  forty  millionth 


MASS.  37 

Mass. — According  to  the  above  explanation,  the  mass  of  a  body 
is  the  quantity  of  matter  of  which  it  is  composed ;  and  on  this 
quantity  depends  its  inertia ;  consequently,  the  amount  of  this 
inertia  gives  the  actual  measure  of  the  mass,  and  here  gravity 
furnishes  us  with  the  best  means  of  ascertaining  the  quantity  we 
seek. 

The  mass  of  a  body  is  always  proportional  to  its  weight.  This 
connection  between  the  two  is  everywhere  demonstrable  by  expe- 
riment, although  we  may  readily  conceive  it  to  be  not  a  necessary 
result.  For,  let  it  be  assumed  that  there  are  bodies  in  nature  on 
which  gravity  exercises  no  power,  on  this  account  they  will  not, 
therefore,  the  less  continue  to  possess  inertia ;  further  let  it  be 
assumed  that  the  force  of  gravity  acts  unequally  upon  the  particles 


part  of  the  earth's  meridian,  expressed  in  toises,  was  taken  as  the  new  unit  of 
length — in  short,  the  relation  of  the  metre  to  the  toise  was  then  accurately  deter- 
mined. 

As  in  the  present  day  the  French  system  of  measures  is  referred  to  in  almost  all 
scientific  works,  we  deem  it  desirable  to  give  a  table  of  the  relations  of  foreign  and 
English  weights  to  those  established  in  the  French  system,  giving  by  way  of  intro- 
duction, a  few  facts  referring  thereto. 

The  metre  is  divided  into  10  decimetres,  100  centimetres,  and  1,000  millimetres. 

The  following  diagram  represents  a  decimetre,  with  its  subdivisions,  as  accurately 
as  we  can  represent  them : — 

Fig.  2. 


10 

The  relation  of  the  most  important  measures  of  length  to  the  metre  are  given  in 
the  following  table : — 

1  English  foot =   304,79  millimetres. 

1  Rhenish  or  Prussian  foot =   313,85          " 

1  Vienna  foot =  316,10          « 

1  Paris  foot =  324,84          « 

1  Toise  =  6  French  feet =   1,94904  metres. 

1  German  or  geographical  mile =        7407 

1  English  nautical  mile  =  1  Italian  mile  .  .  =  1852  " 
The  measures  for  solid  and  fluid  bodies  and  the  weights  are  all  derived  from  the 
measure  of  length  in  the  French  system.  Thus  the  unit  of  the  fluid  measure  is  the 
litre  (2,113  pts.)  =  1,000  cubic  centimetres.  A  cubic  centimetre  of  water  weighs 
1  gramme  (or  15.44  grains  troy);  1,000  grammes  make  1  kilogramme;  1  litre  of 
water,  therefore,  weighs  1  kilogramme  (2,679  Ibs.  troy). 

One  gramme  is  equal  to  10  decigrammes  =  100  centigrammes  =  1,000  milli- 
grammes (15.44  grs.  troy). 

The  pound  weight  differs  considerably  in  different  countries,  but  it  may  on  an 
average  be  said  to  correspond  pretty  nearly  with  the  half  kilogramme.   The  Baden 

4 


38 


PROPERTIES    OF    BODIES. 


of  different  substances,  and  that  a  ball  of  lead  is  only  heavier  than 
a  ball  of  wood  of  equal  size  because  gravitation  acts  more  espe- 
cially upon  the  particles  of  the  lead,  without,  on  that  account, 
the  mass  of  the  leaden  ball  being  greater  than  that  of  the  wooden 
ball.  Again,  to  make  the  subject  clearer,  let  us  suppose  two 
equally  large  balls,  one  of  lead,  the  other  of  wood,  and  let  us 
assume  that  the  mass  or  amount  of  inertia  be  the  same  in  both,  it 
clearly  follows  that  in  this  case  the  leaden  ball  would  fall  with  the 
greater  velocity,  for  we  know  that  it  weighs  some  twelve  times 
more  than  the  wooden  ball,  and  that,  consequently,  the  force 
which  impels  the  former  is  twelve  times  as  great  as  that  which 


and  Hesse  pound  is  exactly  this  weight,  as  the  system  of  measures  adopted  in 
these  countries  has  been  derived  from  the  French.    This  pound  of  500  grammes  is 
the  standard  measure  used  in  the  German  Zollverein,  or  general  customs. 
1  London  pound  (troy  weight)     .     =   373,202  grmes. 
1  Vienna  pound  (trade  weight)     .     =   572,880      " 

1  Old  French  pound =  489,503      " 

1  Prussian  pound =  467,711      " 

[To  render  the  comparison  of  the  English  and  French  weights  still  more  evident, 
the  following  tables  are  subjoined. 


.015444  grains. 

.15444  « 
1.5444 

15.444  " 

154.44  « 

1544.4  « 
15444. 


.03937  inches. 

.39371  « 
3.9371 

39.371  « 
393.71 

3937.1  " 

39371.  « 


.061028  cubic  in. 
.61028         « 
6.1028 

61.028  « 

610.28 
6102.8 
61028.  «    1 


Milligramme  .  .  . 
Centigramme  .  .  . 
Decigramme  .  .  . 
Gramme  

WEIGHTS. 

=  0.001  grammes 
=   0.01           " 
=   0.1             « 
=    1                « 
=    10              « 
=   100           " 
=   1000         " 

Decagramme  .  .  . 
Hectogramme  .  .  . 
Kilogramme  .  .  . 

Millimetre 

Centimetre 

Decimetre 

Metre 

Decametre 

Hectometre 

Kilometre 


Millilitre 

Centilitre 

Decilitre 

Litre   .     . 

Decalitre 

Hectolitre 

Kilolitre 


MEASURES  OF  LENGTH. 

=  0.001  metres.  = 

=  0.00  «  = 

=  0.1  «  = 

=   1  «  = 

=   10  "  = 

=   100  "  = 

=   1000  «  = 

MEASURES  OF  CAPACITY. 

=     0.001  Litre.  = 

=     0.01  "  = 

=     0.1  « 

=     1  « 

=     10  " 

=     100   •  «  = 

=     1000  «  = 


DENSITY.  39 

acts  upon  the  latter,  and  would,  therefore,  induce  greater  velocity, 
if  equal  resistance  were  opposed  to  both  balls.  We  find,  how- 
ever, that  the  leaden  ball  falls  no  faster  than  the  wooden  one,  at 
least  in  vacuo,  and  hence  we  see  that  the  force  which  impels  the 
former,  although  twelve  times  as  great,  acts  against  a  body  pos- 
sessing twelve  times  the  inertia  of  wood.  And,  as  we  find  that 
the  rapidity  with  which  all  bodies  fall  in  vacua  is  equal,  we  con- 
clude, on  the  same  grounds,  that  the  mass  of  a  body  is  always 
proportionate  to  its  wreight,  and  that,  therefore,  the  weight  of  a 
body  is  a  measure  of  its  mass. 

Density. — The  density  of  a  body  is  the  relation  of  its  weight 
to  its  volume,  and  thus  conveys  the  idea  of  specific  gravity,  which 
is  a  constant  characteristic  property  of  every  substance.  As  it 
was  necessary  to  choose  one  body  in  particular  as  the  unit  of 
density,  to  which  all  others  might  be  compared,  water  in  its  con- 
dition of  greatest  density  has  been  made  choice  of  for  this  pur- 
pose. The  density,  or  specific  gravity,  of  a  body  is,  therefore,  the 
number  which  indicates  how  much  heavier  a  body  is  than  an 
equal  volume  of  water.  A  cubic  centimetre  of  iron  weighs  7.8,  a 
cubic  centimetre  of  gold  19.258  grammes,  while  an  equal  volume 
of  water  weighs  only  one  gramme ;  therefore  7.8  is  the  specific 
weight  of  iron,  and  19.258  that  of  gold.  Hence  to  find  the 
specific  gravity  of  a  body,  we  divide  its  absolute  weight  by  the 
weight  of  an  equal  volume  of  the  water. 

Thus  the  data  necessary  to  determine  the  specific  gravity  of  a 
body  are  its  absolute  weight  by  the  weight  of  an  equal  volume  of 
water. 

These  data  are  most  readily  obtained  for  fluids.  If  we  take 
a  narrow-necked  vessel  and  fill  it  up  to  a  certain  marked  line 
on  the  neck,  first  with  water,  and  then  with  the  fluid  to  be  deter- 
mined, and  weigh  it  each  time  in  a  balance,  we  obtain  the  rela- 
tive weight  of  the  two  fluids.  Thus,  if  we  wish  to  ascertain  the 
specific  gravity  of  oil  of  vitriol,  we  must  first  place  the  empty 
bottle  on  one  scale  and  counterbalance  it,  then  fill  it  to  the  gra- 
duated line  with  water.  If  we  assume  that  the  bottle  contain 
exactly  one  litre,  that  is  1000  cubic  centimetres,  the  water  will 
weigh  exactly  1000  grammes.  If,  now,  we  fill  the  bottle  to  the 
same  point  with  oil  of  vitriol,  it  will  require  1848  grammes  to 
make  the  balance  even.  Since  the  oil  of  vitriol  in)  the  flask  weighs 


40  PROPERTIES    OF    BODIES. 

1848  grammes,  while  an  equal  volume  of  water  weighs  only  1000 

grammes,  the  specific  gravity  of  the  former  is  =*  1.848. 

1000 

[This  rule  is  applicable  with  some  modifications  when  our 
usual  weights  are  employed.  Thus  when  the  specific  gravity  of 
a  fluid  is  to  be  ascertained,  it  can  be  readily  accomplished  by 
taking  a  bottle  of  convenient  size,  and  carefully  counterbalancing 
it.  The  weight  of  water  required  to  fill  it  is  then  to  be  ascer- 
tained, and  then  the  combined  weight  of  the  bottle  and  the  fluid 
under  examination ;  on  subtracting  from  the  latter  weight  that  of 
the  bottle,  the  weight  of  the  fluid  will  be  afforded.  If  this  weight 
be  divided  by  that  of  water  1000,  the  quotient  will  be  the  specific 
gravity.  For  instance,  a  counterbalanced  bottle  holds  500  grains 
of  water,  and  412  grains  of  alcohol,  then  412-^-500  =  0.824— for 
500  :  1000  ::  412  :  0-824.] 

Owing  to  the  difficulty  of  always  obtaining  sufficiently  large 
quantities  of  the  fluids  to  be  weighed  in  so  capacious  a  vessel, 
and  the  damage  to  a  fine  balance  in  support- 
ing such  heavy  masses,  it  is  more  expedient 
to  make  use  of  smaller  vesssels.  The  form 
commonly  employed  is  represented  in  Fig.  3. 
This  vessel  is  made  to  contain  from  eight  to 
twenty  cubic  centimetres,  and  has  a  ground 
glass  stopper  made  of  a  part  of  a  thermometer 
tube,  in  order  to  admit  of  the  rising  of  por- 
tions of  the  fluid  in  case  of  expansion  by  heat 
through  the  slender  opening  without  the  stopper  being  raised,  or 
the  bottle  burst. 

In  order  to  determine  the  specific  gravity  of  solid  substances 
we  must  form  from  them  a  body  of  regular  shape,  as  a  cube  or 
sphere,  in  order  to  estimate  the  more  readily  its  cubic  contents. 
The  absolute  weight  of  such  bodies  is  found  by  the  balance,  and 
the  weight  of  an  equal  volume  of  water  is  given  by  the  known 
volume  of  the  body.  If  a  cube  of  marble  weigh,  for  instance, 
21.6  grammes,  and  each  of  its  sides  be  two  centimetres,  its  cubic 
contents  will  be  eight  cubic  centimetres ;  a  cube  of  water  of  like 
size  will  thus  weigh  eight  grammes ;  and,  consequently,  the  spe- 

21  6 

cific  gravity  of  the  marble  is  to  that  of  water  as  — —  =2.7 

8 

Take  a  sphere  of  dried  beechwood  weighing  25.79  grammes, 


SPECIFIC    GRAVITY.  41 

and,  supposing  its  diameter  to  be  four  centimetres,  we  may  easily 
compute  its  cubic  contents,  which  we  shall  find  to  be  33.49 
cubic  centimetres.  A  sphere  of  water  of  equal  size  will,  there- 
fore, weigh  33.49  grammes,  and  the  specific  gravity  of  the  wood 

9^  7Q 

is  therefore,  ^11T  =  0.77. 
'  33.49 

As,  however,  it  is  not  always  possible  to  obtain  such  large 
quantities  of  substances,  and  it  is  sometimes  impracticable  to 
form  bodies  of  the  regularity  of  figure  necessary,  other  methods 
must  be  resorted  to  for  ascertaining  the  specific  gravity ;  and  the 
majority  of  these  depend  upon  hydrostatic  laws,  the  consideration 
of  which  we  must  postpone  to  a  subsequent  period.  (Chap.  III. 
Hydrostatics.)  The  following  method,  however,  is  not  grounded 
upon  these  principles,  and  is  often  made  use  of  to  ascertain  the 
specific  gravity  of  such  bodies  as  can  only  be  obtained  in  small 
portions. 

We  first  fill  the  vessel  (Fig.  3)  with  water,  and  bring  it  into 
equilibrium  in  the  balance,  then  lay  the  granules  beside  it,  and 
ascertain  the  absolute  weight.  This  done,  we  remove  both  from 
the  scale,  and,  throwing  the  granules  into  the  water  in  the  bottle, 
again  insert  the  stopper.  A  quantity  of  water  will  then  escape, 
equal  in  bulk  to  the  granules  which  have  displaced  it.  On 
weighing  a  second  time,  we  ascertain  the  quantity  of  water  that 
has  been  displaced ;  or,  in  other  words,  the  weight  of  a  volume 
of  water  equal  to  the  volume  of  the  granules. 

By  way  of  illustration,  let  us  determine  the  specific  gravity  of 
platinum  granules  as  they  occur  in  nature  : — 

The  glass  vessel  with  water  weighs  .     .     13.52     grms. 
The  granules 4.056      " 

Both  together 17.576      " 

If,  after  throwing  the  granules  into  the  bottle,  putting  the  stopper 
in,  and  weighing  the  whole  together,  we  find  it  to  be  17.316 
grammes,  the  weight  of  the  water  forced  out  by  the  granules  must 
be  17.576—17.316  =  0.26  gram.;  consequently  the  specific 

gravity  of  the  granules  is  — '. =  15.6. 

The  same  method  may  be  pursued  with  larger  portions  of  bodies 
if  a  suitable  vessel  be  chosen  for  the  experiment. 


42  PROPERTIES    OF    BODIES. 

If  the  body  to  be  weighed  be  soluble  in  water,  some  fluid  must 
be  chosen,  as  alcohol,  oil  of  turpentine,  or  some  other  in  which 
the  body  does  not  dissolve.  By  the  above-described  process,  we 
find  how  much  a  certain  quantity  of  fluid  weighs  which  has  the 
same  volume  with  the  body  to  be  weighed,  and  when  once  the 
specific  gravity  of  the  fluid  is  known,  it  is  easy  to  ascertain  the 
weight  of  an  equal  volume  of  water. 

Let  it  be  assumed  that  a  piece  of  salt  which  is  insoluble  in  oil 
of  turpentine  weigh  0.352  gram.,  and  displaces  when  put  into  the 
glass  0.13  gram,  of  oil  of  turpentine.  The  specific  gravity  of  this 
fluid  is  0.8725 ;  an  equal  volume  of  water  will  therefore  weigh 

0  13 
— -1 =  0.149,  and  the  specific  gravity  of  the  salt  is,  therefore, 


COMPOSITION   OF   FORCES.  43 


SECTION    II. 

EQUILIBRIUM    OF    FORCES. 


CHAPTER    I. 

EQUILIBRIUM   AND    DECOMPOSITION    OF    FORCES    IN    THE    SO 
CALLED  SIMPLE   MACHINES. 

A  BODY  is  in  a  state  of  equilibrium  when  all  the  forces  acting 
upon  it  counteract  each  other,  or  when  their  action  is  prevented 
by  any  resistance.  In  a  body  suspended  by  a  thread,  the  action 
of  gravity  is  destroyed  by  the  resistance  of  the  thread.  If  the 
thread  be  not  strong  enough,  it  will  break,  and  the  body  will  fall 
to  the  ground.  A  body  may  often  be  in  equilibrium  without 
having  any  fixed  point  of  support,  and  without  any  apparent 
resistance.  The  fish  may  be  in  a  state  of  equilibrium  in  the 
water,  and  the  balloon  in  the  air,  but  here  the  gravity  is  counter- 
acted by  a  pressure,  of  which  we  shall  further  speak. 

It  may  be  said  that  all  bodies  which  appear  to  be  in  a  state  of 
rest  are  acted  upon  by  many  mutually  counteracting  forces.  It 
falls  to  the  department  of  statics  to  ascertain  the  conditions  of 
equilibrium,  while  the  subject  of  dynamics,  on  the  other  hand, 
investigates  the  lawrs  of  the  motions  which  result  when  the 
conditions  requisite  for  the  establishment  of  equilibrium  are  not 
satisfied. 

In  order  to  measure  forces  we  must  assume  some  arbitrary 
force  as  unity. 

Two  forces  are  equal  when,  in  acting  upon  one  point  from 
opposite  directions,  they  remain  in  equilibrium.  Two  equal  forces 
acting  in  the  same  direction  are  equal  to  a  double  force.  We 
should  have  a  triple  force  if  three  equal  forces  acted  in  the  same 
direction,  and  so  on. 


44  STATICS. 

Whatever  be  the  number  of  forces  acting  upon  one  point,  and 
whatever  their  direction  may  be,  they  can  only  impart  one  single 
movement  in  one  definite  direction.  Hence  we  assume  that  there 
is  a  force  which  is  capable  in  itself  of  producing  the  same  action 
as  these  combined  forces,  and  consequently  of  replacing  them. 
This  is  termed  the  resultant.  For  example,  when  a  ship  is  im- 
pelled by  the  combined  action  of  the  stream,  the  rudder,  and  the 
wind,  it  moves  in  a  definite  direction;  but  if  the  actions  of  the 
stream,  rudder,  and  wind  were  to  cease,  we  could  evidently  im- 
part the  same  motion  to  the  vessel  by  attaching  to  it  a  rope  or 
line  by  which  a  definite  force  might  be  made  to  bear  in  the  direc- 
tion towards  which  the  ship  was  impelled  by  the  simultaneous 
action  of  the  three  forces.  This  then  is  the  resultant  of  the  three 
forces. 

The  combination  of  forces  which  act  together  upon  one  point, 
we  term  a  system  of  forces,  or,  when  speaking  of  them  in  refer- 
ence to  the  resultant,  we  .call  them  component  or  lateral  forces. 
It  is  evident  that,  if  we  were  to  add  to  the  combined  system  of 
forces  a  new  force,  equal  and  opposed  to  the  resultant,  all  the 
forces  acting  in  concert  must  retain  their  equilibrium.  If,  for 
example,  to  abide  by  our  former  illustration,  we  had  caused  a 
force  to  act  upon  the  line  of  the  vessel  which  was  equal,  but  op- 
posed, to  the  resultant  force  of  the  stream,  rudder,  and  wind,  the 
newly-applied  force  would  induce  a  state  of  equilibrium,  and  the 
ship  would  remain  at  rest  just  as  if  it  were  lying  at  anchor. 

If  two  or  more  forces  act  in  the  same  direction  their  resultant  is 
the  sum  of  the  separate  forces.  When  two  forces  act  in  opposite 
directions  upon  one  point,  the  resultant  is  equal  to  the  difference 
of  the  two,  and  will  act  in  the  direction  of  the  greater. 

If  the  directions  of  two  forces  acting  upon  a  material  point, 
make  an  angle  with  each  other,  we  find  the  resultant  by  means 
of  a  law  known  under  the  name  of  the  parallelogram  of  forces, 
and  established  by  means  of  the  following  simple  consideration : — 
Suppose  two  forces  acting  simultaneously 
on  the  point  a,  one  in  the  direction  a  x, 
the  other  in  the  direction  a  y.     Let  one 
force  be  such  that  in  a  given  time — say  a 

_ _x___    second — it  will  by  itself  move  the  point 

from  a  to  6,  while  the  other  force  will, 
in  the  same  period  of  time,  move  it  by  itself  from  a  to  c.     If 


PARALLELOGRAM   OF    FORCES.  45 

now  the  point  be  exposed  for  a  second  to  the  simultaneous  action 
of  both  forces,  the  effect  is  evidently  the  same  as  if  the  point 
were  subjected  for  one  second  to  the  sole  action  of  the  one,  and 
the  next  second  to  the  sole  action  of  the  other  force.  The  first 
force  alone  impels  the  point  from  a  to  b  in  one  second ;  and  if  the 
action  of  this  force  were  to  cease  at  the  instant  the  point  reaches 
by  and  the  point  be  then  solely  subjected  to  the  action  of  the 
second  force,  it  would,  at  the  close  of  another  second,  reach  r. 
Hence,  if  both  forces  act  simultaneously,  the  point  a  must,  in  the 
course  of  a  second,  reach  the  same  point  r. 

An  illustration  will  make  this  more  evident.     A  ship  acted 

Fig.  5. 


upon  simultaneously  by  two  forces,  the  stream  and  wind,  starts 
from  the  point  A  on  the  side  of  a  river.  Let  us  assume  that  the 
vessel  will  be  urged  obliquely  across  the  river  by  the  action  of  the 
wind  alone,  in  a  definite  time,  say  a  quarter  of  an  hour,  going 
from  A  to  B  ;  and  assume  it  to  be  borne  during  the  same  period 
of  time  by  the  force  of  the  stream  alone,  if  there  were  no  wind 
from  A  to  C ;  then  it  would  in  the  same  period  of  time  go  from  A 
to  D,  if  both  wind  and  stream  acted  simultaneously,  that  is,  it 
must  reach  the  point  D  in  a  quarter  of  an  hour,  when  impelled  by 
the  simultaneous  action  of  the  two  forces,  as  it  would  have  gone 
from  A  to  B  in  a  quarter  of  an  hour,  if  acted  upon  solely  by  the 
wind,  and  from  B  to  D  during  the  next  quarter  of  an  hour  when 
impelled  only  by  the  stream. 

The  line  a  r  (Fig.  6)  is  the  diagonal 
of  the  parallelogram  a  b  r  c,  which  by 
means  of  the  law  we  have  mentioned  may 
be  thus  expressed. 

The  resultant  of  two  forces  which  simultaneously  act  at  any 
angle  upon  a  material  point  is  such  as  to  tend  to  move  the  point 


46  STATICS. 

through  the  diagonal  of  the  parallelogram,  which  we  may  con- 
struct from  the  lines  corresponding  to  each  of  the  component  or 
lateral  forces. 

As  the  line  which  a  body  passes  over  in  a  given  time  is  pro- 
portionate to  the  force  which  impels  it,  and  as  in  determining 
the  resultant  we  only  endeavor  to  find  its  direction  and  relations 
of  size  to  both  component  forces,  the  law  maybe  thus  expressed: 
— "If  two  lines  be  drawn  in  the  direction  of  two  forces,  and 
through  their  point  of  contact,  and  their  length  to  be  proportionate 
to  the  respective  forces,  the  diagonal  of  the  parallelogram  which 
is  determined  by  these  two  lines  will  represent  the  resultant  both 
in  magnitude  and  direction." 

As  a  state  of  equilibrium  must  be  established  between  three 
forces,  if  each  be  equal  and  opposed  to  the  resultant  of  the  other 
two,  we  may  easily,  by  means  of  an  experiment  pertaining  to 
statics,  test  the  correctness  of  the  law  of  the  parallelogram  of 
forces. 

To  the  leaf  of  a  table  there  are  attached  two  vertical  rods,  each 

of  which  has  a  movable  slide 
Flg>  7-  bearing   a    pulley  that   turns 

easily  upon  its  axis  in  a  verti- 
cal plane.  The  rods  must  be 
so  screwed  on  that  the  vertical 
planes  of  both  pulleys  coincide. 
If  now  we  have  a  line  over  the 
pulleys,  attaching  at  one  end  a 
weight  a,  at  the  other  end  a 
weight  c,  and  lastly,  a  weight 
b  between  the  pulleys,  the 
whole  will  be  in  a  state  of  equilibrium  in  any  definite  position  of 
the  threads;  we  have  three  forces  acting  upon  the  point  o  in  the 
directions  o  p,  o  q,  and  o  r,  and  it  is  easy  to  ascertain  whether 
those  relations  between  the  amount  and  direction  of  the  forces 
really  exist,  such  as  the  law  of  the  parallelogram  offerees  requires. 
Supposing  by  way  of  illustration,  that  a  =  2  and  c  =  3  ounces, 
how  great  must  be  the  force  at  b  if  the  angle  p  o  q  be  75°  ? 
According  to  the  above  law  the  resultant  may  easily  be  obtained, 
by  construction,  as  in  Fig.  8. 

If  the  angle  r  s  t  measure  75°,  and  r  s  =  2  and  s  t  =  3 
(some  unit  being  assumed),  we  shall  find  that  the  diagonal 


PARALLELOGRAM    OF    FORCES. 


47 


s  p  =  4.  Thus,  if  the  angle  p  o  q  =  75°,  the  weight  6  must 
be  equal  to  4  ounces ;  and  if  we  at- 
tach a  weight  of  4  ounces  to  the  string, 
we  shall  find  that  the  angle  p  o  q  will 
measure  75°;  and  this  we  may  easily 
prove  by  holding  a  figure  of  larger 
dimensions  behind  the  thread,  r  s  cor- 
responding with  o  p,  and  s  t  with  o  q. 
If  b  had  been  made  larger  than  4,  and 
all  the  other  parts  of  the  figure  were 
left  unaltered,  the  angle  p  o  q  would 
be  less  than  75°  ;  and  the  smaller  we 
make  the  weight  at  6,  the  larger  will 
be  the  angle  p  o  q. 

When  both  forces  are  equal,  the  resultant  divides  the  angle 
which  they  make  with  each  other  into  two  equal  parts. 

When  the  two  forces  are  unequal,  the  resultant  divides  their 
angle  into  unequal  parts,  approaching  more  nearly  to  the  direc- 
tion of  the  larger  force. 

As  we  can  find  the  resultant  of  two  forces  acting  upon  a  point, 
so  it  is  likewise  easy  to  ascertain  the  resultant  of  any  given 
number  of  forces,  nothing  more  being  necessary  than  to  find  the 
resultant  of  the  two  first  forces,  then  their  resultant  with  the  third 
force,  and  so  on. 

As  two  forces  can  be  replaced  by  a  single  force,  so  conversely, 
we  may  substitute  two  forces  for  one ;  and  we  see  further,  that  an 
infinite  number  of  different  systems  of  forces  may  have  the  same 
resultant,  and  conversely,  that  one  force  may  be  replaced  in 
innumerably  different  ways  by  a  sys- 
tem of  two  forces.  But  if  it  were 
required  that  the  force  a  r  should  be 
replaced  by  two  other  forces,  one  of 
which  should  have  the  direction  a  y, 
and  the  magnitude  a  c,  the  problem 
is  perfectly  definite,  there  being  but 
one  way  to  complete  the  parallelogram, 
and  to  find  the  component  or  lateral  force  a  b. 

From  the  parallelogram  of  forces  are  derived  the  laws  of  equi- 
librium in  all  simple  machines;  and  thes  we  now  proceed  to 
describe. 


Fig/9. 


48 


STATICS. 


The  Inclined  Plane  affords  a  practical  illustration  of  the  decom- 
position of  forces.  When  a  weight  rests  upon  a  plane,  which 
forms  an  angle  x  with  the  horizon,  the  gravity  of  the  body  acting 
in  the  direction  a  b  is  no  longer  at  right  angles  to  the  plane,  and, 
consequently,  the  latter  has  not  to  support  the  full  pressure  of  the 

Fig.  10. 


weight  of  the  load.  In  fact,  the  gravity  of  the  body  may  be  de- 
composed into  two  forces,  the  one  of  which  acts  at  right  angles 
with  the  plane,  causing  the  pressure,  while  the  other,  acting 
parallel  with  the  inclined  plane,  urges  the  body  down  it.  The 
magnitude  of  these  two  forces  may  easily  be  obtained  by  con- 
struction. If  a  6  represent  the  magnitude  and  the  direction  of 
gravity,  we  have  only  to  draw  a  line  at  right  angles  with  the  in- 
clined plane  through  a,  and  another  parallel  with  it,  then  join  b 
and  d,  and  drop  the  perpendicular  b  c.  The  line  a  d  represents 
the  amount  of  pressure  which  the  plane  has  to  support,  a  c  the 
amount  of  force  which  impels  the  load  down  the  inclined  plane, 
or,  in  other  words,  the  pressure  upon  the  plane,  and  the  force 
which  tends  to  move  the  body  parallel  to  the  inclined  plane  are 
to  the  weight  of  the  body  as  the  lines  a  d  and  a  c  are  to  a  b. 

But  the  triangle  a  b  c  is  similar  to  the  triangle  jR  S  T  and  a  b: 
a  c  =  R  S:  S  T,  and,  consequently,  the  force  which  urges  the 
body  down  the  inclined  plane  is  to  its  weight  as  the  height  of  the 
plane  is  to  its  length.  If  we  denote  by  x  the  angle  which  the 
inclined  plane  makes  with  the  horizon,  then  it  is  evident  that 
a  c  =  a  b  sin.  x  and  b  c  =  a  b  cos.  x;  and,  therefore,  if  P  repre- 
sents the  weight  of  the  body,  the  pressure  which  the  plane  has  to 


INCLINED    PLANE.  49 

support  is  equal  to  P  cos.  x,  and  the  force  that  urges  the  body 
down  the  plane  is  equal  to  P  sin.  x. 

We  will  attempt  to  make  this  point  clearer  by  the  following 
illustration.  If  we  lay  a  load  in  a  little  carriage,  and  place  it 
upon  an  inclined  plane,  it  will  roll  down ;  this  may,  however,  be 
hindered  by  attaching  to  the  carriage  a  line,  passing  round  a 
pulley,  and  having  the  weight  P  suspended  from  its  other  ex- 
tremity. Supposing  the  little  carriage  and  its  load  to  weigh  100 
ounces,  and  the  angle  x  to  be  30°,  then  S  T  =  J  R  S,  and, 
consequently,  a  c  =  J  a  b;  that  is  to  say,  the  force  which  urges 
the  carriage  down  the  plane  is  equal  to  the  half  of  its  weight, 
and  the  carriage  will,  therefore,  be  prevented  from  rolling  down, 
if  we  make  the  weight  P  equal  to  50  ounces. 

If  the  angle  x  were  19°  30',  then  would  S  T  =  J  R  S,  and 

100 

then  the  weight  P  need  only  be  —  =  33  ounces  to  prevent  the 

o 

carriage  from  rolling  down  the  plane. 

As  sin.  14°  30'  nearly  =  J,  that  is  to  say,  when  the  angle 

x  =  14°  30'  S  T=  i  R  S,  in  this  case  P  must  =  l—  =  25 

4 

ounces. 

In  order  to  make' experiments  with  reference  to  different  angles 
of  inclination,  we  must  use  a  polished  board,  which,  by  means  of 
a  hinge,  is  so  secured  to  a  fixed  horizontal  board  as  to  admit  of 
being  placed  at  any  angle  of  inclination  that  may  be  required. 
The  pulley  round  which  the  line  is  passed  may  be  secured  to  the 
board,  but  we  may  also  easily  make  use  of  one  of  the  rods  in  Fig. 
7  for  this  purpose,  as  the  slide  may  be  pushed  up  and  down  to 
raise  or  depress  the  pulley  to  the  elevation  required.  Instead  of 
attaching  the  weight  P  directly  on  the  line,  we'  lay  it  in  a  scale 
which  has  been  weighed,  and,  together  with  its  contents,  must  be 
made  equal  to  the  computed  weight  P. 

We  daily  see  the  practical  application  of  the  inclined  plane. 
Every  road  leading  up  an  ascent  is  an  inclined  plane,  on  which 
weights  are  lifted  from  valleys  to  the  summit  of  hills  ;  for  instance, 
in  order  to  draw  a  loaded  wagon  up  a  hilly  road,  besides  the 
force  necessary  to  overcome  the  friction  (which  is  likewise  required 
upon  even  ground),  we  must  apply  another  force  to  sustain  the 
equilibrium  with  that  portion  of  gravity  acting  parallel  with  the 
inclined  plane,  and  which  increases  with  the  steepness  of  the  road. 
5 


50 


STATICS. 


For  this  reason  it  is  preferable  to  make  a  road  winding  circuit- 
ously  round  a  hill,  instead  of  carrying  it  directly  upward.  It  fre- 
quently happens  in  erections  of  almost  every  kind  that  the  mate- 
rials for  building  are  raised  to  the  required  height  by  means  of 
inclined  planes.  This  application  of  the  inclined  plane  was 
known  to  the  ancients ;  and  it  is  highly  probable  that  the  Egypt- 
ians availed  themselves  of  it  in  order  to  raise  the  huge  blocks  of 
stone  which  they  employed  in  constructing  their  pyramids. 


Fig.  11. 


Fig.  12. 


The  Screw  is  an  inclined  plane  wound  round  a  cylinder.  Let  a  b  c, 
Fig.  12,  be  a  rectangular  piece  of  paper  whose  horizontal  side,  a 
5,  is  equal  to  the  circumference  of  the  cylinder,  Fig.  11,  the  paper 
be  so  wound  around  the  cylinder  that  a  b  shall  form  the  periphery 
of  its  base,  the  hypothenuse  a  c  will  wind  round  the  cylinder  in 
an  uniformly  ascending  curved  line,  o  p  q  r;  if  the  point  a  coin- 
cide with  the  point  o,  b  will  also  coincide  with  o,  and  c  will  be 
vertically  over  o  at  r.  The  curved  line  o  p  q  r,  which  is  repre- 
sented in  our  figure,  is  termed  the  thread  of  the  screw ;  and  its 
reverse  side  has  been  drawn  white  in  order  to  show  that  the  entire 
curvature  of  the  line  from  o  to  r,  is  the  distance  of  two  contigu- 
ous threads. 

If  we  imagine  a  triangle  continued  along  the  thread  of  the  screw 
round  the  cylinder,  we  obtain  a  screw  with  a  triangular  thread,  as 
shown  in  Fig.  13;  and,  if  we  suppose  a 
Fig.  13.  Fig.  14.  parallelogram  wound  in  like  manner  round 
the  cylinder,  we  have  a  flat-threaded  screw, 
as  represented  in  Fig.  14.  A  screw  cannot 
by  itself  be  applied  to  remove  or  lift  heavy 
weights,  or  to  exercise  any  strong  pressure ; 
for  to  effect  these  purposes  it  must  be  so  com- 
bined with  a  screw-box  or  nut  (which  is 
a  concave  cylinder,  on  the  interior  of  which  a 


THE    SCREW.— THE    WEDGE.  51 

corresponding  spiral  cavity  is  cut),  that  the  elevations  of  the  one 
may  accurately  fit  into  the  depressions  of  the  other.  If  we  suppose 
the  screw  to  be  fixed  vertically,  then  every  revolution  must  cause 
an  elevation  or  depression  of  the  nut.  If  a  wqjght  lying  on  the  nut 
should  be  raised  by  the  turning  of  the  screw,  it  is  evident  that  the 
same  principles  are  at  work  here,  as  in  an  inclined  plane  of  equal 
elevation.  The  steepness  of  the  convolutions  of  the  screw  is 
inversely  proportional  to  the  distance  between  two  contiguous 
threads  as  compared  with  the  circumference  of  the  cylinder. 

The  screw  is  used  partly  to  lift  heavy  weights,  and  partly  to 
sustain  great  pressure,  the  resistance  acting  in  some  cases  upon 
the  screw  itself,  and  in  others  upon  the  screw-box.  In  estimating 
the  effect  of  a  screw,  we  must  not  lose  sight  of  the  fact  that  fric- 
tion plays  a  conspicuous  part  in  its  action ;  but  of  this  we  shall 
speak  presently.  In  order  to  make  use  of  the  screw  as  a  power- 
ful machine,  the  turning  force  is  not  applied  directly  to  the  cir- 
cumference, but  to  a  lever,  or  arm,  as  we  may  observe  in  all 
screw-presses. 

The  Wedge. — Another  form  of  applying  the  inclined  plane  is 
the  wedge,  which  is  used  to  cleave  wood  and  masses  of  stone.   By 
thrusting  wedges  under  their  keels,  ships 
are  raised  for  the  purpose  of  being  re-  Flg>  15' 

paired  in  the  docks.  The  wedge  is  the 
principal  agent  in  the  oil-mill.  The  seeds 
from  which  the  oil  is  to  be  extracted  are 
introduced  into  hair  bags,  and  placed 
between  pieces  of  hard  wood.  Wedges  inserted  between  the  bags 
are  driven  in  by  allowing  heavy  beams  to  fall  on  them.  The 
pressure  thus  excited  is  so  intense  that  the  seeds  in  the  bags  are 
formed  into  a  mass  nearly  as  solid  as  wood.  All  our  cutting 
implements,  as  knives,  chisels,  scissors,  are  nothing  more  than 
wedges.  It  must  be  perfectly  clear  to  every  one  that  the  action 
of  the  wedge  may  be  referred  to  that  of  the  inclined  plane. 

The  Pulley  is  a  round  thin  disc,  hollowed  out  on  its  edges,  and 
turning  upon  an  axis  passing  through  its  centre  at  right  angles 
with  its  plane. 

We  divide  pulleys  into  the  fixed  and  movable.  Fixed  pulleys 
are  such  as  have  an  immovable  axis,  and  simply  allow  of  things 
being  turned  round  them.  If  a  string  or  line  be  passed  round  a 
part  of  the  circumference  of  a  fixed  pulley,  and  forces  act  at  either 


52 


STATICS. 


Fig.  16. 


extremity,  a  state  of  equilibrium  will  not  be  brought  about  unless 
the  force  which  stretches  the  line  on  the  one 
side  be  equal  to  the  force  acting  on  the 
>  other.  Fig.  16  represents  a  pulley,  c,  mov- 
ing round  a  fixed  axis,  and  the  line  stretched 
by  forces  acting  in  the  directions  a  b  and  d 
e.  If  we  suppose  the  lines  d  e  and  a  b  pro- 
longed to  their  intersecting  point,  m,  it  is 
evident  that  if  m  were  a  point  connected 
with  the  pulley,  we  could  change  the  points 
of  application  of  the  two  forces  from  a  and  d 
to  m  without  altering  anything  in  the  action ; 
and  thus  we  should  have  two  forces  meeting 
at  m,  which  could  only  be  in  equilibrium  if  their  resultant  were 
so.  If  the  two  forces  meeting  in  m,  and  acting  in  the  directions 
m  b  and  m  e,  are  equal,  their  resultant  will  bisect  the  angle  b  m  e, 
and  will  then  pass  through  the  fixed  central  point  c,  and  we  shall 
have  a  condition  of  equilibrium.  If  one  of  the  two  forces  be 
greater  than  the  other,  the  resultant  will  no  longer  pass  through 
the  fixed  point,  and  consequently  equilibrium  will  not  be  main- 
tained. 

The  pressure  which 
the  axis  of  the  pulley  has 
to  sustain  must  clearly 
be  equal  to  the  resultant 
of  the  two  forces  ;  and  if 
the  directions  of  the  forces 
be  parallel,  as  in  Fig.  17, 
the  pressure  upon  the 
axis  is  equal  to  the  sum  of 
the  two  forces,  in  which 
we  might  also  include  the  weight  of  the  pulley.* 


Fig.  17. 


Fig.  18. 


*  It  might  be  objected  that  this  is  arguing  in  a  circle ;  for  we  have  already  used 
the  pulley  as  an  experimental  illustration  of  the  correctness  of  the  proposition  of  the 
parallelogram  of  forces,  and  now  we  derive  the  conditions  of  equilibrium  in  a  pulley 
from  the  parallelogram  of  forces.  This,  however,  is  not  so  unreasonable  as  it  may 
at  first  sight  appear ;  for,  although  the  conditions  of  equilibrium  between  all  the 
forces  acting  on  a  pulley  can  only  be  understood  in  all  their  bearings  by  means  of 
the  theory  of  the  parallelogram  of  forces,  we  may  easily  perceive,  even  without  any 
knowledge  of  these  laws,  that  the  powers  acting  on  both  ends  of  a  string  (the  ten- 
sion of  the  string  remaining  constant)  passed  round  a  pulley  must  be  equal  if  they 


THE   PULLEY. 


53 


Fig.  19. 


Fig.  20. 


A  movable  pulley  cannot  be  in  equilibrium  unless  the  forces 
by  which  the  two  ends  of  the  string  are  stretched  are  equal  to  one 
another,  for  in  this  case  only  does  their  result- 
ant pass  through  the  central  point  of  the  disc. 
The  action  of  this  resultant  is  not  arrested 
owing  to  the  fixed  condition  of  the  axis,  but 
owing  to  there  being  a  third  power  in  the  axis 
in  the  direction  of  the  resultant,  which  is 
equal  and  opposed  to  it.  This  third  power 
is  usually  applied  to  a  hook  fastened  on  the 
block.  At  Fig.  18  it  is  represented  by  a 
weight. 

When  the  two  ends  of  the  line  passing 
round  the  movable  pulley  are  parallel  to  each 
other,  as  in  Fig.  19,  it  is  evident  that  the  force 
with  which  each  end  is  drawn,  is  half  as  great 
as  the  weight  hanging  to  the  block.  When 
two  groups  of  pulleys,  of  which  the  one  is 
fixed,  and  the  other  movable,  are  so  con- 
nected by  a  line  that  the  latter  may  pass  from 
the  one  to  the  other,  we  have  a  system  of  pul- 
leys. 

Fig  20  represents  a  system  consisting  of 
three  fixed  and  three  movable  pulleys.  The 
weight  q  which  is  attached  to  the  common 
block  of  the  three  movable  pulleys  is  sup- 
ported by  the  six  lines  which  connect  the 
upper  and  lower  pulleys ;  and  consequently, 
as  the  weight  is  equally  divided  between  the 
lines,  each  is  drawn  by  one-sixth  of  the  weight 
q  ;  and  if  sixty  pounds  weight  were  suspended 
to  the  bottom,  each  line  would  be  drawn  upon 
by  a  force  of  ten  pounds. 

If  we  observe  the  external  line  to  the  left 
side  which  connects  the  lowest  of  the  mov- 
able pulleys  with  the  highest  of  those  that  are 


are  to  be  in  equilibrium ;  for,  as  each  force  tends  to  turn  the  pulley  iu  an  opposite 
direction,  a  state  of  equilibrium  can  only  be  brought  about  when  these  forces  are 
equal,  as  must  already  have  been  made  evident  to  all  in  our  illustration  in  Fig.  7. 

5* 


54 


STATICS. 


Fig.  21, 


fixed,  we  shall  see  that  this  line  runs  round  the  top  pulley,  and 
hangs  freely  down  on  the  right  side.  Now,  in  order  to  establish 
a  state  of  equilibrium,  it  is  necessary  that  the  tension  of  the  line 
should  be  equal  on  the  two  sides  of  the  upper  pulley  ;  and  as  we 
have  seen  that  the  line  to  the  left  is  drawn  with  the  force  of  one- 
sixth  of  the  weight  at  q,  it  is  necessary  to  attach  a  weight  equal 
to  one-sixth  of  q  to  the  end  of  the  line,  in  order  to  obtain  a  state 
of  equilibrium.  We  may,  therefore,  again  poise  a  weight  of 
sixty  pounds,  by  attaching  to  the  line  a  weight  of  ten  pounds. 

As  the  amount  of  weight  bearing  upon  the  lines  depends  upon 
their  number,  that  is  the  number  of  pulleys  composing  the  system, 
it  follows  that  another  relation  will  be  established  between  the 
forces  and  weights,  but  this  can  readily  be  obtained  by  a  similar 
mode  of  deduction. 

The  Lever. — Suppose  a  line  passed  round  a  pulley,  to  the  end 
of  which  the  weighty  (Fig.  21)  is  attached  ;  whilst,  on  the  other 
side,  the  line  is  drawn  in  the  direction  a  6,  with  a  force  equal  to 

the  weight  p.  Here,  how- 
ever according  to  the  theory 
of  the  parallelogram  offorces, 
we  may  decompose  the  forces 
meeting  at  a,  and  acting  in 
the  direction  a  6,  into  lateral 
forces,  one  of  which  acts  in 
the  direction  of  d  from  a, 
being  a  prolongation  of  the 
direction  of  the  radius  m  a, 
while  the  direction  of  the 
other  force  a  f  is  parallel 
with  g  p. 

If  the  pulley  be  fixed,  the 
action  of  the  force  a  d  will  be 
counteracted  by  the  resist- 
ance of  the  fixed  central 
point  m ;  we  may,  therefore,  entirely  remove  the  component  force 
acting  in  the  direction  a  d,  without  disturbing  the  equilibrium, 
and  we  may  replace  the  active  force  a  b  by  its  component  force 
acting  in  the  direction  of  a  f. 

If  the  line  a  c  represent  the  force  p  acting  in  the  direction  a  b, 
then  the  line  a  /will  give  the  amount  of  the  component  force  P, 


THE    LEVER.  55 

and,  without  further  working  out  the  relations  of  size  between  a  c 
and  a  f  or  p  and  P,  we  see  at  once  that  P  must  be  larger  than 
p;  we  might,  therefore,  without  disturbing  the  equilibrium,  re- 
place the  force  p,  acting  in  the  direction  a  b  by  another  force  P, 
likewise  acting  at  a,  but  in  a  vertical  direction. 

Instead  of  letting  the  force  P  act  directly  at «,  we  may,  without 
disturbing  the  equilibrium,  choose  any  part  of  the  line  a  f  as  the 
point  of  application ;  we  may,  for  instance,  let  the  force  P  act  at 
the  point  A,  where  the  lines  af  and  g  m  intersect  each  other,  and 
thus  we  have  two  rectangular  forces  p  and  P  in  a  state  of  equili- 
brium, at  the  ends  of  a  straight  line  h  g  revolving  round  m. 

The  two  forces    are  unequal,  as  their  Fi    22 

respective  points  of  application  at  h  and  g 
are  at  unequal  distances  from  the  fulcrum 
m.  We  have  now  to  ascertain  the  relation 
which  exists  between  the  magnitude  of  the 
forces  p  and  P,  and  the  lengths  h  m  and 
g  m.  The  triangles  c  af,  Fig.  21,  and  a  A  m  are  similar  to  each 
other,  and  hence  a  c  :  af  =  hm  :  a  m.  But  the  lengths  a  c  and 
a  f  are  to  each  other  as  the  forces  p  and  P;  thus  we  have 

p  :  P  =  h  m  :  a  m, 
and  since  a  m  =  g  m, 

p:  P  =  h  m  :  gm, 
or 

p:P=L:l   .     .     .     .     (1), 

if  we  make  the  length  h  m  =  L  and  g  m  =  I.  Or,  to  express 
the  same  fact  inwards,  we  may  say  that  the  forces  P  and  p  bear 
an  inverse  ratio  to  the  distances  of  their  points  of  application  from 
the  fulcrum  m. 

A  straight,  inflexible  rod  turning  on  a  fixed  point  is  called  a 
lever.  If  two  opposite  forces  at  right  angles  to  its  direction  be 
applied  at  two  different  points  of  a  lever,  a  state  of  equilibrium 
will  be  established  when  the  above  condition  has  been  fulfilled. 
The  distance  of  the  point  of  application  of  a  force  from  the  fulcrum 
is  called  the  arm  of  the  lever ;  and  we  may,  therefore,  thus  ex- 
press the  condition  of  equilibrium  in  the  lever :  Two  forces  tend- 
ing to  draw  the  lever  in  opposite  directions  are  in  equilibrium 
when  they  bear  an  inverse  proportion  to  the  corresponding  arms 
of  the  lever. 

If,  for  instance,  the  arm  h  m  (Fig.  22)  was  half  the  length  of 


56  STATICS. 

g  m,  then  P  must  be  twice  as  large  as  p.  A  force  p  may  be  in 
equilibrium  with  a  hundredfold  larger  force  P  if  the  arm  m  g  be 
100  times  as  long  as  the  arm  h  m. 

From  the  proportion  (1),  it  follows  that  P  L  =  p  I,  that  is 
to  say,  in  order  that  two  forces  in  a  lever  shall  be  in  equilibrium, 
it  is  necessary  that  the  products  of  the  force  and  the  distance 
at  which  it  acts  from  the  fulcrum  be  equal  for  both  forces.  If, 
for  instance,  the  force  p  =  6  ounces,  and  the  arm  be  12  inches, 
it  would  be  necessary,  in  order  to  bring  them  to  a  state  of 
equilibrium,  to  have  on  the  other  side  an  arm  three  times  shorter, 
that  is,  4  inches,  acted  on  by  a  force  three  times  greater,  that  is, 
3  X  6  =  18  ;  it  is  evident  that  the  product  6  12  is  equal  to  the 
product  4  x  18. 

The  product  obtained  by  multiplying  the  force  by  the  arm  of 
the  lever  is  called  the  static  moment  of  the  force.  We  may  also 
define  the  static  moment  of  a  force  as  that  force  which,  acting  at 
an  arm  of  one  unit  on  the  opposite  side  of  the  fulcrum,  shall  pre- 
serve the  state  of  equilibrium. 

In  Fig.  23,  if  we  assume  that  the  force  to  the  right  =  6,  and 

the   arm  of  the   lever  =  5,  the 
23-  static  moment  of  the  force  will  be 

-i — \ — H^  5  x  6  =  30 ;  then,  if  the  force  on 
the  left  hand  is  to  be  in  a  state  of 
equilibrium  with  the  former,  the 
static  moment  of  the  two  must  be 
equal,  and  the  force  acting  on  the  left 
side  on  an  arm  equal  to  3  must  have  a  value  of  10.  But,  instead 
of  letting  the  force  6  act  on  the  arm  of  length  5,  we  might,  with- 
out disturbing  the  equilibrium,  apply  a  force  of  30  on  the  arm  of 
length  1 ;  and,  in  like  manner,  the  force  10  acting  on  the  other 
side  of  the  lever,  which  equals  3,  may  be  replaced  by  a  force  ot 
30  acting  at  an  arm  equal  to  1. 

When  several  forces  act  on  each  side  of  the  fulcrum,  a  state  of 
equilibrium  will  be  established,  if  the  sums  of  the  static  moments 
on  each  side  be  equal.  For  example,  in  Fig.  24  m  is  the  fulcrum, 

and  on  one  side  the  force  5 

Fig.  24. 

acts  on  the  arm  2,  the  force  2 

I — I — I — »    J^    ' — I — ' — I — i — I       on  the  arm  4,  and  the  force 

IB  ran  pj|       Hi        ill    4  on  the  arm  6,  while  on  the 

s  ^      other  side  the  forces  10  and 


l 


STATICS.  57 

3  act  on  the  arm  3  and  4.  Now,  all  these  forces  will  be  in  a 
state  of  equilibrium,  for  the  sums  of  the  static  moments  of  both 
sides  are  equal.  The  sum  of  the  static  moments  on  the  one  side  is 
5x2  +  2x4  +  4x6  =  42,  and  the  sum  of  the  same  forces 
on  the  other  side  is  10  x  3  +  3  x  4  =  42.  Instead  of  the  force 
5,  which  acts  at  the  distance  2,  we  might  have  the  force  10  at 
the  distance  1 ;  thus  also  the  forces  2  and  4,  acting  at  the  dis- 
tances 4  and  6,  may  be  replaced  by  two  other  forces,  8  and  24, 
acting  at  right  angles  to  arm  1.  We  may  likewise  substitute  the 
forces  10,  8,  and  24,  acting  at  the  distance  1,  for  the  forces  5,  2, 
and  4,  acting  at  the  distances  2,  4,  and  6  respectively;  or,  in 
other  words,  we  may  replace  the  three  forces  5,  2,  and  4,  acting 
on  their  different  arms,  by  one  single  force  of  42,  acting  at  the 
distance  1.  On  the  other  side  we  may  also  substitute  two  forces, 
30  and  12,  acting  at  an  arm  1,  for  the  forces  10  and  3,  acting  at 
the  distances  3  and  4 ;  or  we  may  make  use  of  a  single  force  of 
42,  acting  at  a  distance  1.  As  the  sums  of  the  static  moments 
are  equal  on  both  sides,  a  state  of  equilibrium  must  be  maintained. 

The  common  steelyard  furnishes  us  with  a  good  example  of  the 
application  of  the  lever,  and  Fig.  25  may  serve  to  elucidate  the 
principles  of  this  machine. 

A  lever  is  movable    about  Flg*  25> 

the  point  a,  while  a  scale  is 
suspended  at  r,  to  receive 
the  weight  acting  upon  the 
arm  a  r,  and  this  weight  is 

kept  in  equilibrium  by  a  sliding  weight  at  the  other  arm  of  the 
lever.  The  heavier  the  weight  is,  the  further  must  the  sliding 
weight  be  removed  from  the  fulcrum  r. 

In  such  a  lever  as  we  have  been  considering,  the  fulcrum  has 
to  sustain  a  resistance  equal  to  the  sum  of 
the  forces  on  both  sides;  it  may  also  be  in 
equilibrium  when  the  fulcrum  is  not  fixed, 
but  is  moved  by  a  power  acting  in  a  con- 
trary direction,  but  equal  to  the  sum  of  the 
other  forces.  Fig.  26  explains  this.  Let 
us  assume  that  c  is  the  fixed  fulcrum  of  a 
lever  m  n,  at  the  ends  of  which  the  forces 
P  and  P  balance  each  other.  Their 
equilibrium  will  not  be  disturbed  by  the  fulcrum  c  ceasing  to  be 


58  STATICS. 

fixed,  if  a  force  n  be  attached  to  it,  which  shall  be  equal  to  the 
sura  of  P  and  P',  and  act  in  an  upward,  as  the  forces  P  and  P' 
draw  in  a  downward  direction. 

We  may  regard  either  of  the  three  points  m,  c,  or  n,  as  fixed 
without  disturbing  the  equilibrium.  If  one  of  the  extreme  points, 
n  for  instance,  be  fixed,  we  have  a  one-armed  lever;  that  is,  one 
in  which  the  two  forces  JV  and  P  act  on  the  same  side  of  the 
fulcrum  n.  The  two  forces  have  in  this  case  opposite  directions, 
and  the  pressure  upon  the  point  of  support  is  equal  to  the  differ- 
ence of  the  two  forces  P  and  JV.  The  arm  of  the  force  P  is  /  +  /', 
if  we  designate  the  length  m  c  as  /,  and  the  length  n  c  as  /';  the 
arm  of  force  Nis  I'.  If  c  had  been  the  fixed  fulcrum  we  should 
have  had  as  a  requisite  condition  of  equilibrium  : — 

P'  :  P  =  /  :  I1, 
and,  consequently, 

F  +  P  ;  P  =  I  +  I'  :  /', 
or, 

If,  therefore,  the  forces  N  and  P  acting  in  opposite  directions  are 
to  be  in  equilibrium,  they  must  be  inversely  proportionate  to  the 
length  of  the  arms  at  which  they  act. 

Fig.  27  shows  the  applica- 

Flg>  27' ^          tion  of  a  single-armed  lever. 

The  valve  j9,  which  closes  the 
opening  of  a  boiler,  is  forced 
up  by  the  pressure  of  the 
steam,  but  this  pressure  is  equipoised  by  a  much  smaller  force, 
the  weight  n  acting  downwards,  because  r  acts  at  a  longer  arm 
than  the  pressure  on  the  under  surface  of  the  valve. 

Fi    2g  The  two  extreme  points  (Fig.  28)  m  and 

n  of  the  rod  m  n  may  be  fixed,  while  a  force 
N  acts  at  e;  so  that  the  point  m  has  a  pres- 
sure J9,  and  the  point  n  a  pressure  p'  to  sup- 
port. W^hen  two  men  carry  a  load  hanging 
to  a  rod,  each  one  supporting  an  end  of  the 
rod  on  their  shoulders,  they  have  between 
them  the  whole  weight  to  carry ;  and  when 
it  hangs  exactly  in  the  middle  of  the  pole,  it  will  be  equally 
divided  between  them ;  but  if  the  load  should  be  hung  nearer  to 
one  of  them,  he  will  have  the  most  weight  to  support.  Supposing 


\Yt 

J| 
*»• 


STATICS.  59 

that  the  appended  load  weigh  100  Ibs.,  the  pole  be  5  feet  long, 
and  that  the  load  hang  2  feet  from  one,  and  three  feet  from  the 
other  end,  then  the  shoulders  of  one  bearer  will  have  to  support  a 
pressure  of  60  Ibs.,  and  those  of  the  other  a  pressure  of  40  Ibs. 

We  have  hitherto  only  considered,  the  forces  acting  at  right 
angles  to  the  lever ;  equilibrium  may,  however,  be  established 
without  this  being  the  case. 

In  Fig.  29  7i  is  the  fixed  point  Fig.  29. 

of  the  lever  a  b ;  at  a  the  force  o  ^ 

p  acts  in  the  direction  a  c,  and 
at  b  the  force  q  in  the  direction  a/ 

b  d,  the  forces  p  and  q  bearing 
the  same  relations  to  each  other 
as  the  lines  a  c  and  b  d.  Ac- 
cording to  the  law  of  the  pa- 
rallelogram of  forces,  p  may  be 
decomposed  into  two  forces,  of 

which  the  one  p'  acts  at  right  angles  to  a  6,  while  the  other  acts 
in  the  direction  of  a  b.  In  the  same  way  q  may  be  decomposed 
into  two  forces,  of  which  one  q'  acts  at  right  angles  to  a  6,  and  the 
other  in  the  direction  of  that  line. 

The  action  of  the  two  component  forces  which  act  in  the  direc- 
tion of  the  line  a  b  is  evidently  fully  counteracted  by  the  resist- 
ance of  the  fixed  point  n,  thus  leaving  only  the  action  of  the 
forces  j/  and  q.1  We  may,  therefore,  substitute  the  component 
forces  p'  and  q',  acting  at  right  angles  to  the  lever,  in  place  of  the 
original  forces  p  and  q.  A  state  of  equilibrium  will  be  established 
if  p'  and  q'  correspond  in  an  inverse  ratio  to  the  length  of  their 
arms — that  is,  if 

pf  :  qf  =  n  6,  n  a 
or  if 

q'  x  n  b  =  p'  x  n  a. 

If  we  prolong  the  direction  of  the  force  p,  and  draw  n  o  (  =  1) 
perpendicular  to  it,  we  have  the  triangle  a  o  n,  which  is  similar 
to  the  triangle  whose  hypothenuse  is  p,  and  one  of  whose  sides  is 
p' ;  and  from  this  it  follows  that 

p  :  p'  —  a  n  :  I 
and  consequently  that 

p  x  /  =±=  pf  x  a  n. 
The  force  jt),  acting  obliquely  on  the  arm  a  n,  acts  exactly  the 


60  STATICS. 

same  as  the  component  force  p'  acting  at  the  same  point  a ;  and 
also  as  if  the  force  p  acted  at  right  angles  to  a  shortened  arm, 
which  is  found  by  letting  fall  a  perpendicular  from  the  fulcrum  n 
upon  the  direction  of  the  force. 

The  moment  of  an  oblique  force  is  found  by  multiplying  the 
force  by  the  perpendicular  let  fall  upon  the  direction  of  the  force 
from  the  axis. 

Thus  the  oblique  force  q  acts  as  if  it  met  the  arm  of  the  lever 
n  m  at  right  angles,  and  the  two  forces  p  and  q  are  in  equilibrium 
when  p  x  o  n  —  q  x  n  m. 

Fi    3Q  By  the  same  process,  we  find  the  mo- 

ment of  the  forces  when  the  lever  does  not 
form  a  straight  line.  When  any  fixed  sys- 
tem turns  round  a  fixed  axis,  the  forces 
that  tend  to  turn  it  round  the  axis  follow 
N  the  laws  of  the  lever ;  and  these  we  there- 
fore find  applied  in  many  machines,  which  may,  therefore,  be 
divided  into  more  or  less  complicated  systems  of  levers.  In  the 
windlass  and  capstan  (Figs.  31  and  32)  the  weight  r  corresponds 
to  the  counteracting  force  p  in  an  inverse  ratio  to  the  arms  of  the 
lever ;  that  is,  inversely  to  the  radii  a  b  and  c  d.  If,  for  ex- 
ample, the  radius  a  b  of  the  axle  is  four  times  less  than  the  radius 
c  d  of  the  wheel,  we  may  equipoise  a  weight  of  100  Ibs.  by  a 
force  of  25  Ibs. 

Fig.  31.  Fig.  32. 


The  capstan  (Fig.  32)  only  differs  from  the  windlass  by  having 
its  revolving  axis  placed  vertically,  and  thus  a  comparatively 
small  force  is  required  at  p  to  move  the  weight  r. 

When  two  parallel  forces  acting  at  right  angles  to  a  lever  are 
equipoised,  the  equilibrium  will  not  be  disturbed  if  we  increase  or 


CENTRE    OF    GRAVITY.  61 

diminish  them  in  equal  proportions,  or  if  we  keep  the  forces 
parallel  to  each  other  in  altering  their  direction.  If,  for  instance, 
the  forces  a  b  =  p  and  c  d  =  q,  acting  Fi  33 

on  the  lever  a  c,  are  equipoised,  the          c ^      a 

equilibrium  will  not  be  disturbed  if  we 
let  the  forces  act  in  the  parallel  direc- 
tions a  e  and  c  f,  for  the  oblique  force 
p  acts  in  the  same  manner  as  its  rec- 
tangular component  pf,  and  the  oblique 
force  q  as  the  rectangular  force  q' ;  and  pr  q1  will  certainly  main- 
tain a  condition  of  equilibrium  if  it  exists  between  the  forces  p 
and  q,  acting  perpendicularly  to  the  lever. 

Centre  of  Gravity. — A  heavy  body,  whatever  be  its  size,  may 
be  regarded  as  a  combination  of  innumerable  material  points, 
acted  upon  by  gravity.  All  these  forces,  although  innumerable, 
may  be  replaced  by  one  single  force  acting  at  a  fixed  point. 
This  single  force,  which  is  nothing  more  than  the  sum  or  the 
results  of  all  the  individual  actions  of  gravity,  is  termed  the 
weight  of  a  body,  and  the  point  at  which  the  resultant  acts  the 
centre  of  gravity. 

This  definition  is  sufficient  to  prevent  weight  and  gravity  from 
being  confounded.  Gravity  is  the  elementary  force  which  acts 
directly  upon  all  the  particles  of  matter,  while  the  weight  of  a 
body  is  the  sum  of  the  actions  which  gravity  exercises  upon  this 
body. 

It  is  very  important  to  be  able  to  ascertain  the  weight  of  bodies 
and  their  centre  of  gravity,  since  we  can  then  substitute  one 
single  force,  namely,  the  weight,  for  all  the  elementary  forces 
acting  on  the  body ;  and  one  single  point,  namely,  the  centre  of 
gravity,  for  the  collective  points  forming  the  body.  We  may 
thus  consider  a  heavy  mass,  whatever  be  its  size  and  form,  as  a 
single  point,  on  which  one  single  force  acts. 

In  a  heavy  body,  possessing  an  extension  of  even  some  hun- 
dred yards,  the  direction  of  gravitation  will  be  not  only  perfectly 
parallel  for  all  the  molecules,  but  also  perfectly  equal  for  all, 
because  all  the  molecules  will  fall  with  equal  velocity  in  vacuo. 
The  centre  of  gravity  is  consequently  nothing  more  than  the  centre 
of  parallel  and  equal  forces,  where  the  position  does  not  change 
when  the  position  of  the  body  with  respect  to  the  direction  of 
quantity  changes. 
6 


62 


CENTRE    OF    GRAVITY. 


Fig.  34. 


We  deduce  from  the  laws  of  the  action  of  parallel  forces  the 
fact  that  every  solid  body  must  have  such  a  centre  of  gravity.  If 
an  immovable  straight  line  a  b  (Fig.  34)  be 
supported  at  its  centre  and  loaded  at  both 
ends  with  equal  weights,  the  whole  will  be 
in  equilibrium,  in  whatever  direction  the 
line  be  turned  round  the  point  at  which  the 
central  force  acts,  whether  the  line  be  in 
the  position  a  b,  or  in  the  position  a  V .  Let 
us  assume  that  the  two  points  a  and  b  are 
two  heavy  molecules,  connected  by  the 
straight  rigid  rod  a  b,  supposed  devoid  of 
weight ;  then  it  is  clear  that  equilibrium  must  occur  if  only  the 
point  c  be  supported,  whatever  be  the  position  of  the  line  a  b. 
The  point  c  would  be  nothing  more  than  the  centre  of  gravity  of 
the  body  consisting  of  the  two  molecules.  We  may  regard  the 
actions  of  the  forces  of  gravity  of  the  two  molecules  combined  at 
the  centre  of  gravity,  without  on  that  account  the  equilibrium 
being  disturbed.  If  at  the  three  angles  of  a  rigid  triangle,  a  b  c 

(Fig.  35),  supposed  to  be  devoid  of 
weight,  three  equal  and  parallel  forces 
are  at  work,  it  is  easy  to  ascertain 
the  position  of  their  central  force. 
We  may  unite  the  two  forces  acting 
at  b  and  c  in  the  centre  d  of  the  line 
b  c  without  disturbing  the  equili- 
brium, and  thus  the  action  of  the 
three  forces  is  reduced  to  the  action 
of  the  two  acting  at  the  points  a  and 
d.  The  force  acting  at  d  is  twice  as 
great  as  that  at  a;  if,  therefore,  we  divide  the  line  a  d,  pass- 
ing through  the  point  m,  into  two  parts,  of  which  the  one  a  m  is 
twice  as  long  as  the  remaining  part  d  m,  a  state  of  equilibrium 
will  necessarily  be  established  between  the  parallel  forces  2  p 
and  jo,  acting  at  d  and  a,  if  only  the  point  m  be  supported,  what- 
ever be  the  position  of  the  line  a  d.  But  as  the  force  acting  at  d 
is  only  the  resultant  of  the  parallel  forces  at  b  and  c,  we  may 
take  these  forces  themselves  instead  of  their  resultant ;  and  thus 
it  is  clear  that  the  three  parallel  forces  acting  at  a,  6,  and  c  must 
be  in  equilibrium  if  the  point  m  be  supported,  or  if  a  force  equal 


Fig.  35. 


CENTRE    OF    GRAVITY. 


63 


to  3  p,  acting  in  an  opposite  direction,  be  applied  at  w,  what- 
ever may  be  the  position  of  the  triangle  in  other  respects. 

If  we  assume  that  a,  6,  and  c  are  three  heavy  molecules,  which 
must  necessarily  always  retain  the  same  relative  position  towards 
each  other,  then  the  gravity  of  these  molecules  will  act  in  the 
same  manner  as  the  weights  attached  at  a,  &,  and  c,  and  it  is  evi- 
dent that  the  body  consisting  of  the  three  molecules  will  be  in 
equilibrium  if  only  its  centre  of  gravity  m  be  supported. 

Exactly  as  we  can  demonstrate  that  two  or  three  firmly  united 
molecules  must  have  a  centre  of  gravity,  we  can  likewise  com- 
prehend that  every  4,  5,  6,  &c.,  firmly-united  molecules  must  have 
such  a  centre  of  gravity,  and,  further,  that  every  solid  body  must 
have  a  fixed  point  of  that  nature,  whatever  be  the  number  of 
molecules  of  which  it  is  composed. 

The  only  requirement  necessary  to  the  equilibrium  of  a  heavy 
body  is  that  its  centre  of  gravity  should  be  supported.  If,  there- 
fore, the  centre  of  gravity  of  a  body  be  a  fixed  point,  the  body 
will  always  be  in  equilibrium,  in  whatever  manner  we  may  turn 
it.  We  may  prove  this  by  means  of  a  homogeneous  disc,  made  to 
revolve  round  a  horizontal  fixed  axis,  passing  through  its  centre 
of  gravity.  If  a  body  be  supported  at  a  point  that  does  not  coin- 
cide with  its  centre  of  gravity,  it  may  still  be  in  equilibrium, 
although  only  in  two  special  positions,  when  the  centre  of  gravity 
lies  vertically  above  or  below  the  point  of  support.  This  experi- 
ment is  also  easily  made  by  means  of  a  disc. 

From  these  considerations  we  may  deduce  a  method  which 
will  enable  us  to  show  by  experiment  how  to  find  the  centre  of 
gravity  of  a  body.     If  we 
suspend    the    body  at   a          Fig<  36' 
point  a  (Fig.  36),  the  di- 
rection  of  the  thread  sup- 
porting it  will  pass  through 
a  part  c  on  the  margin  of 
the  body.     The  centre  of 
gravity  must   necessarily 
be  in  the  line  a  c.     Now 
if  we  suspend  the  body  at 
the  point  b  (Fig.  37),  the 
centre  of  gravity  will  be 
again  in  the  line  of  pro- 


64 


CENTRE    OF    GRAVITY. 


longation  of  the  thread,  that  is,  on  the  line  b  d.  The  centre  of 
gravity  lies,  therefore,  at  the  point  of  intersection  of  the  lines  b  d 
and  a  c.  It  is  easy  to  find  the  centre  of  gravity  of  homogeneous 
flat  discs  by  this  method,  but  it  is  difficult  in  other  bodies  to  as- 
certain exactly  the  line  of  prolongation  of  the  thread  through  the 
interior  of  the  body. 

The  centre  of  gravity  of  homogeneous  bodies  of  regular  form 
can  be  decided  by  simple  geometrical  considerations. 

The  centre  of  gravity  of  a  straight  line  lies  evidently  in  the 
middle  of  its  length. 

The  centre  of  gravity  of  a  homogeneous  triangle  (Fig.  38)  is 
found  by  drawing  straight  lines  from  two  of  its  angles  to  bisect 
the  opposite  sides.     The  point  of  intersection  g  of  these  two  lines 
is  the  required  centre  of  gravity.     The  truth  of  this  assertion  is 
easily  proved.    The  point  m  is  the  centre 
of  gravity  of  the  straight  line  6  c.    If  now 
we  suppose  any  straight  line  drawn  pa- 
rallel with  &  c  in  the  triangle,  it  will  evi- 
dently be  bisected  by  the  line  am;  on 
the  line  a  m  lie,  therefore,  the  centres  of 
gravity  of  all  the  lines  in  the  triangle 
parallel  with  be;  and  a  m  is,  so  to  speak, 
a  line  of  gravity  of  the  triangle,  and  the 

centre  of  gravity  must  evidently  lie  in  a  m.  This  reasoning 
shows,  however,  also,  that  the  centre  of  gravity  must  lie  in  the 
line  a  b. 

The  point  g  is  so  situated  that  g  m  =  %  a  m,  and  gn  =  J  bn. 
To  prove  this,  let  the  line  m  nbe  drawn,  it  is  evident  that  m  n  — 
\  b  a.  But  the  triangles  g  m  n  and  g  a  b  are  similar,  and  hence 
it  follows  that  g  m  :  g  a  =  m  n  :  b  a.  Consequently,  that  g  m 


Fig.  38. 


Fig.  39. 


The  centre  of  gravity  of  a  polygon  (Fig.  39) 
is  found  by  dividing  the  figure  into  triangles, 
and  then  determining  the  centre  of  gravity  of 
each  triangle.  As  the  forces  acting  upon  the 
centres  of  gravity  of  the  triangles  are  propor- 
tional to  the  area  of  the  triangles,  we  have 
only  to  seek  the  resultant  of  these  forces  by 
the  rules  already  laid  down. 

The  centre  of  gravity  of  a  triangular  pyra- 


EQUILIBRIUM. 


65 


Fig.  41. 


Fig.  42. 


mid  (Fig.  40)  is  found  by  drawing 
lines  from  the  angle  s  and  a  towards 
the  centres  of  gravity  g-  and  g1  of  the 
opposite  triangles.  The  point  of  in- 
tersection g"  of  these  two  lines  is  the 
centre  of  gravity.  It  is  easy  to  prove 
that  g  g"  =  lg  s. 

The  centre  of  gravity  of  a  cone 
(Fig.  41)  with  a  circular  base  lies  on 
the  straight  line,  joining  the  apex 
with  the  central  point  of  the  base, 
and  its  distance  from  the  central 
point  of  the  base  is  J  of  the  whole 
line. 

The  centre  of  gravity  of  a  regular 
prism,  cylinder,  or  sphere,  corre- 
sponds with  the  geometrical  central 
point  of  each. 

Of  Equilibrium. — We  have  already 
seen  that  the  only  requirement  for  the 
equilibrium  of  a  solid  body  is  that  its 
centre  of  gravity  should  be  supported. 
But  this  condition  may  be  fulfilled  in 
various  ways,  according  to  whether 
the  bodies  are  suspended  at  fixed 
points,  or  rest  upon  points  of  support. 
Let  us  suppose  three  holes,  a,  b,  and  c,  in  a  homogeneous  disc 
(Fig.  42),  of  which  the  one;  a,  passes  through  the  centre  of  gra- 
vity. The  disc  will  be  in  equilibrium  in  all  positions,  if  a  fixed 
axis  is  made  to  pass  through  the  hole  a.  In  such  a  case  as  this 
we  have  an  indifferent  equilibrium.  If  the  axis  passes  through 
the  upper  hole,  6,  the  equilibrium  is  stable,  for  if  we  remove  the 
disc  from  this  position  it  will  always  tend  to  return  to  it.  If  we 
turn  the  disc  a  little  round  the  axis  6,  the  centre  of  gravity  is 
moved  to  the  right  or  left  along  the  arc  m  n;  it  is  no  longer  sup- 
ported, because  it  no  longer  lies  vertically  below  6,  and  the  gra- 
vity acting  upon  it  draws  it  back  to  its  position  of  equilibrium. 
If  the  axis  passes  through  the  lower  hole,  c,  complete  equilibrium 
is  not  established,  but  simply  unstable  equilibrium;  for  as  soon  as 
the  centre  of  gravity  is  in  the  least  removed  from  the  vertical, 

6* 


66 


EQUILIBRIUM. 


Fig.  43. 


passing  through  c,  instead  of  returning,  it  describes  a  semicircle 
until  it  reaches  a  point  vertically  placed  below  the  point  c. 

We  may  thus  generally  express  this  result: — A  body  attached 
to  an  axis  may  be  in  a  state  of  stable,  unstable,  or  indifferent 
equilibrium,  according  to  whether  its  centre  of  gravity  lies  below, 
or  above,  or  within  the  axis. 

Let  us  see  what  happens  when  a  disc  is  placed  upon  a  hori- 
zontal or  inclined  plane,  and  assume  that  the  disc  is  so  composed 
of  lead  and  wood  that  its  centre  of  gravity 
lies  in  the  circle  a  b  d.  In  this  case  none 
but  a  stable  or  unstable  equilibrium  can  ex- 
ist ;  the  former  when  the  centre  of  gravity 
rests  at  a,  the  lowest  point  in  the  circumfer- 
ence a  b  d,  and  the  latter  when  the  centre 
of  gravity  is  at  the  highest  point,  6,  of  this 
circle. 

If  the  same  disc  were  placed  on  an  in- 
clined plane  (Fig.  44),  equilibrium 
would  be  established  if  the  centre  of 
gravity  lay  in  the  vertical  plane  p  6, 
passing  through  the  point  of  contact. 
Stable  equilibrium  will  then  be  esta- 
blished when  the  centre  of  gravity  is 
at  the  lowest  point  a,  and  unstable 
equilibrium  when  it  lies  at  the  highest 
point  b. 

If  we  assume  that  the  disc  is  in  a  state  of  unstable  equilibrium, 
and  were  moved  a  Jittle  towards  the  right  side,  it  would  roll  up 
the  inclined  plane  until  the  condition  of  stable  equilibrium  was 
again  re-established.  During  this  apparent  elevation  the  centre 

of  gravity  nevertheless  continues 
to  approach  the  lowest  points. 

When  a  body  stands  upon  the 
ground,  with  a  more  or  less  wide 
base,  the  perpendicular  drawn 
through  its  centre  of  gravity  must 
fall  within  the  base,  if  a  state  of 
equilibrium  is  to  be  established. 
Thus  the  inclined  cylinder 
would  be  in  equilibrium  (Fig. 


Fig.  45. 


THE    BALANCE. 


67 


45),  if  its  height  did  not  exceed  the  shaded  part  of  the  figure ; 
but  it  must  fall  if  its  height  were  such  that  the  centre  of  gravity 
lay  at  b. 

The  broader  its  base  is,  and  the  lower  its  centre  of  gravity  lies, 
the  firmer  will  a  body  stand.  A  four-footed  animal  stands  firmly 
when  the  centre  of  gravity  of  his  whole  body  lies  over  the  paral- 
lelogram of  which  the  four  angles  are  indicated  by  the  position 
of  its  four  feet.  If  a  man  raise  an  arm,  the  position  of  the  centre 
of  gravity  will  be  changed;  and  if  a  bird  project  its  neck,  the 
centre  of  gravity  is  thrown  considerably  forward.  A  man  carry- 
ing a  weight  must  change  his  position  according  to  the  manner  in 
which  he  carries  it.  For  instance,  if  he  bears  the  load  upon  his 
back  (Fig.  46),  he  must  bend  forward ;  if  he  carry  it  in  his  left 
hand  (Fig.  47),  he  must  incline  the  upper  part  of  his  body  to  the 


Fig.  46. 


Fig.  47. 


right,  otherwise  the  direction  of  the  common  centre  of  gravity  of 
the  human  body  and  the  load  would  fall  beyond  the  line  connect- 
ing the  feet,  and  the  man  would  fall. 

The  Balance. — The  common  balance  consists  essentially  of  a 
rod  called  a  beam,  which  revolves  round  a  fixed  horizontal  axis 
inserted  in  its  centre.  When  there  is  no  load  at  either  end,  the 
beam  should  be  in  a  perfectly  horizontal  position.  To  either  end 
of  the  beam,  scale-pans  are  suspended,  which  serve  for  the  recep- 
tion of  the  bodies  to  be  weighed.  If  both  pans  are  equally  loaded, 
the  beam  will  retain  its  horizontal  position ;  but,  if  an  unit  of 
weight  is  laid  upon  one  of  the  pans,  the  beam  will  incline  towards 
that  side. 


68 


THE    BALANCE. 

Fig.  48. 


We  will  now  inquire  how  the  conditions  above  mentioned  can 
be  satisfied.  If  we  first  suppose  that  the  scale-pans  are  removed, 
and  assume  that  the  horizontal  axis  passes  through  the  centre  of 
gravity  of  the  beam,  we  shall  have  a  case  of  indifferent  equili- 
brium, and  the  beam  will  be  in  equilibrium  at  any  angle  with  the 
horizon.  Such  an  arrangement  will  not,  therefore,  fulfil  the  first 
condition,  namely,  that  the  beam  should  assume  a  horizontal  po- 
sition before  the  pans  are  loaded.  This  condition  can  only  be 
fulfilled  if  the  centre  of  gravity  of  the  beam  lie  below  the  fulcrum. 
If  we  draw  a  line  at  right  angles  with,  and  bisecting  the  longer 
axis  of  the  beam,  this  line  must  pass  through  the  fulcrum  of  the 
beam,  and  through  its  centre  of  gravity. 

The  suspension  of  the  pans  makes  no  difference  in  our  reason- 
ing, for  we  may  consider  their  weight  concentrated  at  the  point 
of  suspension,  and  that  they  thus  form  an  integral  part  of  the  beam. 
If  we  unite  the  points  of  suspension  of  the  pans  by  a  straight 

line,  this  line  may  pass 
through  the  fulcrum,  or 
above  or  below  it.  It  is 
most  easy  to  take  into 
consideration  the  first  of 
these  three  cases,  while 
it  is  likewise  the  most  available  for  practical  application ;  we  will, 
therefore,  begin  with  this  case. 

In  Fig.  49  let  a  b  be  the  straight  line  uniting  the  points  of  sus- 


Fig.  49. 


CENTRE    OF    GRAVITY— SUSPENSION.  69 

pension  of  the  pans,  whose  weight  we  regard  as  concentrated  at 
the  points  a  and  6,  and  let  c  be  the  point  at  which  the  beam  is 
suspended,  that  is  to  say,  the  point  of  support ;  and  s  the  centre 
of  gravity  of  the  beam.  If  equal  weights  P  are  suspended  at  a 
and  6,  the  beam  will  remain  in  a  horizontal  position ;  for  we  may 
consider  that  one  of  the  weights  acts  directly  upon  a,  and  the 
other  directly  upon  b,  and  thus  the  common  centre  of  gravity  of 
the  two  weights  P  will  correspond  with  the  point  c;  and  the  com- 
mon centre  of  gravity  of  all  the  weights  suspended  at  c,  that  is 
to  say,  of  the  beam  and  of  the  weights  P,  will  meet  at  a  point 
between  c  and  s;  this  common  centre  of  gravity  lying  vertically 
under  the  point  of  support,  the  equilibrium  is  not  disturbed. 

If  we  apply  an  extra  weight  r  on  one  side,  the  centre  of  gra- 
vity of  the  suspended  weights,  which  we  must  necessarily  con- 
sider as  concentrated  at  the  points  a  and  6,  no  longer  corresponds 
with  c,  but  falls  on  the  line  a  6,  in  the  direction  of  the  extra  weight, 
somewhere  towards  d.  The  common  centre  of  gravity  of  the 
beam  and  the  weights  will  consequently  be  upon  some  point  m 
in  the  line  d  s;  but  since,  while  the  beam  is  horizontal,  the  com- 
mon centre  of  gravity  m  is  no  longer  vertically  beneath  the  point 
of  suspension  c,  the  whole  beam  must  revolve  sufficiently  around 
the  axis  c  to  fulfil  this  condition.  Hence  the  arm  c  a  will  neces- 
sarily rise,  and  the  arm  c  b  sink.  The  angle  which,  on  the  addi- 
tion of  a  slight  excess  of  weight  in  either  pan,  the  beam  makes 
with  an  horizontal  line  is  termed  the  angle  of  deviation.  ' 

We  shall  now  consider  the  points  that  must  be  attended  to  in 
the  construction  of  the  balance,  in  order  to  render  it  sufficiently 
sensitive  ;  that  is  to  say,  in  order  that  a  very  slight  preponderance 
of  weight  may  give  rise  to  a  large  angle  of  deviation. 

1 .  The  centre  of  gravity  of  the  beam  must  lie  as  closely  as  pos- 
sible below  the  centre  of  suspension;  for  if  (the  other  conditions 
remaining  unaltered)  the  centre  of  gravity  s  of  the  beam  is  raised 
upwards,  the  point  m  will  also  be  elevated  vertically,  which  must 
evidently  produce  an  increase  in  the  angular  deviation  of  the 
beam.  A  contrivance  has  been  applied  to  good  balances  by 
which  the  position  of  the  centre  of  gravity  is  regulated.  A  fine 
screw  is  applied  to  the  prolongation  of  the  line  c  s,  on  which  a 
weight  corresponding  to  circumstances  may  be  screwed  up  and 
down,  by  which  a  change  in  the  position  of  the  centre  of  gravity 
is  manifestly  effected. 


70  SENSIBILITY   OF    THE    BALANCE. 

If  this  weight  were  screwed  up  so  far  that  s  corresponded  with 
c,  we  should  have,  either  without  a  load  or  with  an  equal  load  on 
both  sides,  a  case  of  indifferent  equilibrium ;  were  we  now  to 
bring  an  extra  weight  r  on  one  side,  the  point  m  would  fall  upon 
the  line  a  b  (see  Fig.  49) ;  that  is  to  say,  on  the  addition  of  the 
smallest  extra  weight  the  angle  of  deviation  would  become  a  right 
angle,  the  beam  would  be  completely  inverted,  and,  in  short,  the 
instrument  would  cease  to  be  of  any  service. 

2.  The  sensibility  of  the  balance  increases  with  the  length  of  the 
beam.  If  (everything  else  remaining  the  same)  we  were  to  lengthen 
the  beam,  the  distance  c  d  would  be  proportionally  greater,  and 
the  point  m  would  thus  also  be  removed  further  from  the  line  c  s 
in  a  direction  parallel  to  a  b,  and  consequently  the  line  c  m  would 
make  a  larger  angle  with  c  s,  and  the  angle  of  deviation  would 
also  increase.     (It  is  easy  to  see  that  the  angle  m  c  s  is  equal  to 
the  angle  of  deviation.) 

3.  The  beam  must  be  as  light  as  possible.   We  may  suppose  the 
weight  of  the  loads  2  P-f  r  acting  at  the  point  d,  and  the  weight 
of  the  beam,  which  we  shall  designate  as  g,  united  at  s.     The 
position  of  the  common  centre  of  gravity  m  will  now  evidently 
depend  upon  the  amount  of  the  forces  acting  at  the  ends  of  the 
line  d  s.  If  the  weight  g  at  s  and  2  P  +  r  at  d  be  equal,  m  would 
fall  in  the  middle  of  d  s;  but  the  smaller  g  becomes  in  comparison 
with  2  P  +  r,  the  more  must  m  recede  from  d,  and  the  larger  pro- 
portionably  will  the  angle  of  deviation  be.    In  relation  to  the  two 
last  points,  we  are  confined  to  certain  limits  which  we  cannot 
exceed,  since  too  great  a  length  of  the  beam  would  render  the 
balance  inconvenient  for  practical  purposes,  and  too  great  a  degree 
of  lightness  would  deprive  it  of  the  necessary  strength. 

As  a  matter  of  course,  the  greatest  care  must  be  had  in  the 
construction  of  the  balance  to  render  the  two  portions  of  the  beam 
of  equal  length.  As,  however,  slight  errors  cannot  be  avoided, 
we  must  endeavor  to  correct  them  by  means  of  the  method  of 
weighing  which  is  had  recourse  to.  The  best  manner  of  proceed- 
ing in  this  respect  is  probably  the  following : — The  body  to  be 
weighed  is  laid  upon  one  scale-pan,  and  equipoised  by  a  sufficient 
quantity  of  sand,  shot,  or  any  other  substance  laid  in  the  opposite 
scale-pan.  This  done,  the  body  t6  be  weighed  is  then  removed, 
and  in  its  place  so  many  weights  are  substituted  as  to  restore  the 


SENSIBILITY   OF    THE   BALANCE.  71 

balance  to  equilibrium.  These  newly-applied  weights  will  give 
the  accurate  weight  of  the  body,  whether  or  not  the  arms  of  the 
beam  be  equally  long. 

The  fulcrum  is  formed  of  a  steel  knife-edge,  in  order  as  much 
as  possible  to  avoid  friction,  and  the  scale-pans  are  suspended 
from  similar  edges. 


72  ELASTICITY. 


CHAPTER    II. 

MOLECULAR  EQUILIBRIUM. 

WE  have  already  seen  that,  in  order  to  explain  the  aggregate 
conditions  of  bodies,  we  assume  the  existence  of  molecular  forces, 
which  act  continuously  among  the  separate  particles  of  bodies. 
As  long  as  a  body  remains  unchanged  in  its  internal  condition, 
and  as  long  as  the  individual  particles  remain  not  only  at  un- 
changed distances  but  also  in  a  relatively  unchanged  position,  the 
molecular  forces  acting  among  the  individual  particles  must  re- 
main in  equilibrium.  The  equilibrium  established  between  the 
separate  particles  of  solid  bodies  is  stable,  for  a  greater  or  lesser 
force  is  necessary  to  disturb  this  condition. 

As  we  have  already  seen,  the  force  of  cohesion  preponderates 
in  solid  bodies,  holding  their  particles  together,  and  acting  alike 
against  their  displacement  and  separation  ;  it  being  necessary  to 
employ  a  greater  or  lesser  force  to  bring  about  any  such  displace- 
ment or  separation. 

Elasticity. — When  the  particles  of  a  solid  body  have  been 
slightly  drawn  out  of  their  relative  position  by  an  external  force, 
the  previously  existing  state  of  equilibrium  is  not  on  that  ac- 
count entirely  destroyed,  for  the  particles  may  return  to  their 
former  position  when  the  disturbing  force  ceases  to  act.  This 
property  of  bodies,  by  means  of  which  the  molecules  return  to 
their  former  position  when  the  displacement  occasioned  by  an 
external  force  does  not  exceed  certain  limits,  we  term  elasticity. 
The  elasticity  of  solid  bodies  proves  that  the  molecules  are  in  a 
state  of  stable  equilibrium,  since  it  is  only  under  such  circum- 
stances that  a  body  returns  to  its  position  of  rest,  when  the  exter- 
nal disturbing  force  has  ceased  to  act.  All  bodies  are  not  equally 
elastic :  there  are  some  which  perfectly  assume  their  former  posi- 
tion after  even  a  very  considerable  amount  of  displacement,  and 
such  bodies  are  especially  termed  elastic,  as,  for  instance,  India- 


STRENGTH— ABSOLUTE    STRENGTH.  73 

rubber,  steel  and  ivory;  others,  on  the  contrary,  as  lead,  glass, 
&c.,  are  only  elastic  to  a  limited  degree,  not  being  able  to  bear 
any  great  displacement  of  their  particles  without  the  previous 
condition  of  equilibrium  being  disturbed. 

The  displacement  of  the  particles  may  either  be  occasioned  by 
tension,  compression,  or  rotation. 

When  a  proportionately  large  power  is  necessary  to  produce  a 
displacement  of  the  particles  of  a  body,  we  term  the  latter  hard. 
A  body  may  be  both  hard  and  elastic,  as  is  the  case  with  ivory 
and  steel ;  glass,  on  the  contrary,  is  hard  and  but  slightly  elastic. 

A  body  whose  particles  can  be  removed  by  an  inconsiderable 
force,  is  called  soft.  Soft  bodies  maybe  elastic,  as  India-rubber: 
or  they  may  possess  merely  a  small  degree  of  elasticity,  as  is  the 
case  with  moistened  clay.  The  aggregate  condition  of  such  soft 
bodies  may,  in  some  measure,  be  considered  as  an  intermediate 
state  between  perfect  solidity  and  perfect  fluidity. 

If  the  particles  of  a  body  are  displaced  beyond  the  limits  of 
elasticity,  the  connection  hitherto  existing  between  them  either 
ceases  entirely,  or  the  molecules  arrange  themselves  in  a  new 
condition  of  stable  equilibrium.  In  the  first  case  we  call  the 
bodies  brittle,  in  the  next  ductile.  The  external  form  of  brittle 
bodies  cannot  be  permanently  changed  by  pressure,  blows,  &c. ; 
a  perfect  separation  following,  when,  by  means  of  such  external 
causes,  the  molecules  are  displaced  beyond  certain  limits ;  the 
form  of  ductile  bodies  can,  however,  be  permanently  changed  by 
such  mechanical  means,  as  we  see,  for  instance,  in  the  stamping 
of  coins. 

Strength. — The  force  with  which  a  body  resists  the  separation  of 
its  particles  is  termed  its  strength. 

The  connection  existing  between  the  individual  portions  of  a 
solid  body  may  be  removed  by  tearing,  breaking,  twisting,  or 
compressing  it. 

Absolute  strength  is  the  force  by  which  a  body  resists  being 
torn  asunder  when  it  is  stretched  lengthwise.  This  resistance 
evidently  depends  upon  the  diagonal  section  of  the  body  to  be 
severed,  and  is  proportional  to  it,  for  the  connection  of  two,  three, 
four  times  as  many  molecules  must  be  removed  if  the  diagonal 
section  or  area  of  a  body  be  increased  twice,  thrice,  or  four  times. 
In  order,  therefore,  easily  to  compare  the  absolute  strength  of  dif- 
ferent materials,  we  must  assume  some  unit  for  this  area,  and  then 
7 


74  ABSOLUTE    STRENGTH. 

ascertain  how  great  a  force  is  required  to  rend  a  body,  the  area  of 
which  is  equal  to  this  unit.  If  the  area  of  the  body  submitted  to 
the  experiment  be  greater  or  smaller  than  the  area  assumed  as  the 
unit,  the  strength  may  be  reduced  to  the  measure  of  that  unit. 

Muschenbroek  has  made  numerous  experiments  concerning  the 
absolute  strength  of  different  bodies.  The  following  table  gives, 
according  to  his  calculations,  the  weight  required  to  break  a  rod 
of  different  bodies  whose  diagonal  section  is  one  square  centi- 
metre : — 

about  1970  Ibs. 
2190  " 

1288  to  1992  « 
2466  to  3143 
2893  to  3400 
2003 
5965 
7615 
9962 
583 
979 
7317 
8969 

304  to  501 
750  to  1328 

The  great  variation  perceptible  in  the  strength  of  rope  depends 
upon  the  unequal  character  of  the  material  of  wyhich  it  is  made. 
Thin  ropes  are  proportionally  stronger  than  thick  ones,  from  being 
made  of  better  hemp.  Ropes  have  less  firmness  when  wet  than 
when  dry. 

It  will  be  most  safe  to  assume  for  practical  purposes  that  metals 
possess  only  J,  and  wood  J,  of  the  absolute  strength  ascribed  to 
them  in  the  above  table. 

The  force  which  a  body  opposes  to  the  process  of  breaking  is 
its  relative  strength.  In  order  to  break  a  body,  the  force  must  be 
applied  at  right  angles  to  the  direction  of  its  long  axis;  the  body 
to  be  broken  being  supported  only  at  one,  or  at  both,  of  its  ex- 
tremities. 

Fig.  50  represents  a  prism,  which  is  fastened  at  one  end  into 
a  solid  wall,  while  at  the  other  extremity  is  attached  the  weight 
Q  to  break  it.  If  K  represent  the  absolute  strength,  that  is,  the 
force  with  which  the  body  resists  the  force  endeavoring  to  destroy 
it  and  acting  upon  it  in  its  long  axis,  we  may  suppose  this  force 


Linden  wood 

918 

kilogrammes, 

Fir  (Pinus  sylvestris)    . 
White  Pine  (Pinus  abies) 
Oak      . 

1021 
.     601  to     929 
.  1150  to  1466 

« 

1C 

Beech  .... 

.  1349  to  1586 

u 

Ebony 
Copper  wire 
Brass  wire  . 

934 

2782 
3550 

(C 

it 

(C 

Gold  wire    . 

4645 

<( 

Lead  wire  . 

272 

H 

Tin  wire 

457 

ll 

Silver  wire 

3411 
4182 

U 

u 

White  glass 
Rope  .... 

.     142  to     233 
.     350  to     620 

(C 

u 

EQUILIBRIUM   OF    SOLIDS. 


75 


concentrated  at  the  centre  of  gra-  Fig.  50. 

vity  s  of  that  diagonal  section  which 

corresponds  with  the  plane  of  the 

solid  wall.     The  weight  Q  mani- 

fests an  effort  to  turn  the  whole 

body  round  the  under  edge  of  the 

prism  ;  and  thus  acts  at  the  arm  a 

b,  while  the  resistance  applied  at  s 

acts  at  the   arm  a  s;  if  now  the 

resistance   shall    exactly    counter- 

poise the  force,  the  resistance  K 

must  be  inversely  to  the  force  Q  as  the  arm  a  s  is  to  the  arm  a  b. 

If  the  height  of  the  beam  be  represented  by  A,  a  s  =  J  h,  and  if 

the  length  a  &  be  represented  by  /,  we  have 

K  :  Q  =  I  :  %  h 
or, 

K'h 


The  amount  of  strength  K  with  which  the  body  resists  being 
rent  asunder,  depends  upon  the  diagonal  section  of  the  beam.  If 
we  let  k  represent  the  absolute  strength  for  one  diagonal  section 
of  one  square  centimetre,  while  h  is  the  height  and  b  the  breadth 
of  the  beam,  then 

K  =  k  b  h, 
and  therefore, 

k  b  h2 


From  this  formula,  we  see  that  the  force  necessary  to  break  the 
body  varies  in  a  direct  ratio  with  the  breadth  and  the  square  of 
the  height,  and  inversely  with  the  length. 

If  a  beam  be  supported  in  the  middle  by  a  sharp  edge  (Fig.  51,) 
and  be  loaded  at  both  its  extremi-  Fig.  51. 

ties  with  equal  weights  P,  there 
will  exist  a  tendency  to  break  the 
beam  at  its  centre ;  in  order  to  ef- 
fect this,  the  weight  P  acting  at 
each  end  must  be  twice  as  great  as  the  weight  Q,  which  must  be 
applied  to  the  end  of  the  same  beam  if  projected  its  whole  length 
from  a  solid  wall,  as  in  Fig.  50,  since  the  weight  P  acts  upon  a 
lever  only  half  the  length  of  that  supporting  the  weight  Q. 


76  EQUILIBRIUM    OF    SOLIDS. 

The  pressure  which  has  to  be  supported  in  the  middle  is  evi- 
dently 2  P. 

If  the  beam  be  sup- 

52>  ported  at  each  end  as  in 

Fig.  52,  we  may  break 
it  by  attaching  a  weight 
2  P  to  the  middle.  As 
P  =  2  Q,  we  must  ap- 
ply, in  order  to  break  a  beam  supported  at  each  end,  a  force  four 
times  as  great  as  would  be  necessary  to  break  it  if  it  projected 
its  whole  length  from  a  solid  wall,  and  the  force  acted  upon  the 
free  end.  The  force  necessary  for  breaking  it  is  therefore 

4*^. 
21 

By  the  length  of  the  beam  we  understand,  in  the  one  case,  the 
part  projecting  from  the  wall;  and  in  the  other,  the  portion  lying 
between  the  two  points  of  support. 

We  have  not  taken  into  consideration  in  our  calculations  that 
the  beams  bend  before  they  entirely  break.  By  this  bending,  the 
relative  strength  is  considerably  modified,  so  that  the  value  of  the 
relative  strength  computed  according  to  the  above  formulae,  from 
the  known  absolute  strength,  may  vary  considerably  from  the 
reality.  But,  if  these  formulae  do  not  serve  to  compute  directly 
the  amount  of  the  relative  strength,  they  yet  serve  for  a  compa- 
rison of  the  relative  strengths  of  beams  and  rods,  when  formed  of 
the  same  material,  but  of  different  dimensions  ;  for,  however  the 
amount  of  the  absolute  strength  may  be  modified  by  flexibility, 
it  is  always  directly  proportionate  to  the  breadth  and  square  of 
the  height,  and  inversely  so  to  the  length;  therefore,  in  the  for- 
mula 


nothing  is  changed  by  the  flexibility  but  the  value  of  the  constant 
factor  k,  which  must  be  replaced,  not  by  the  value  of  the  absolute 
strength  taken  from  the  above  tables,  but  by  another  factor,  which 
must  be  obtained  by  experiment  for  each  material.  Experiments 
show  that  the  force  necessary  to  break  a  beam  is  four  times  as 
small  as  is  given  by  the  above  formulae,  if  we  substitute  for  k  the 
number  indicating  the  absolute  strength.  The  influence  exercised 
by  flexibility  upon  the  relative  strength  is  also  proved  from  this, 


ADHESION.  77 

that,  if  a  beam  rests  freely  on  both  its  extremities,  it  may  be 
broken  by  a  weight  suspended  from  its  centre,  only  half  the 
amount  of  that  necessary  to  break  it  when  it  is  fixed  at  both  ends, 
and,  consequently,  incapable  of  yielding. 

In  woods,  the  direction  of  the  fibres  has  naturally  also  much 
influence  upon  the  strength. 

Mhesion. — The  same  force  which  holds  together  the  particles 
of  a  solid  body,  acts  also  in  holding  together  the  particles  of  two 
bodies  already  separated,  if  we  are  able  to  bring  them  within  a 
sufficiently  intimate  contact  with  each  other.  Thus  plates  of 
mirrors,  which  are  laid  closely  one  upon  another  after  being 
polished,  often  adhere  so  tightly  that  they  cannot  be  separated 
without  breaking.  In  the  same  manner  two  plates  of  lead,  when 
pressed  together,  will  adhere  almost  as  closely  as  if  they  formed 
one  single  mass,  provided  always  that  the  surfaces  brought  in 
contact  are  perfectly  smooth  and  metallic. 

The  force  thus  connecting  two  bodies  is  termed  the  force  of 
adhesion. 

Adhesion  is  manifested  not  only  between  homogeneous,  but  also 
between  heterogeneous  bodies.  Thus  a  plate  of  lead  and  a  plate 
of  tin,  or  a  plate  of  copper  and  a  plate  of  silver,  combine  to  form 
an  almost  inseparable  whole,  when  their  polished  surfaces  are 
compressed  by  a  heavy  cylinder.  The  adhesion  of  heterogeneous 
bodies  is  most  strongly  manifested  when  a  fluid  is  brought  in 
contact  with  a  solid  body ;  and  the  former  is  solidified  by  the 
cooling  or  evaporation  of  the  dissolving  medium,  as  we  see  exem- 
plified in  the  processes  of  pasting,  gluing,  and  cementing.  It 
often  happens  on  joining  together  two  pieces  of  glass  with  sealing 
wax,  that  on  tearing  the  whole  asunder,  pieces  are  separated  from 
the  glass,  instead  of  the  glass  being  severed  from  the  wax.  If 
we  rub  a  plate  of  glass  with  glue,  the  two  substances  often  ad- 
here so  closely  together,  that  portions  of  the  former  will  be  torn 
away  on  the  contraction  of  the  glue  in  drying. 

If  two  bodies  having  smooth  surfaces  lie  one  upon  the  other, 
any  attempt  to  push  the  one  beyond  the  other  will  be  opposed  by 
the  force  of  adhesion,  which  shows  that  this  latter  force  has  a 
share  in  the  resistance  of  friction,  which  opposes  itself  wherever 
two  bodies  glide  over  each  other,  or  where  one  body  rolls  over 
another.  We  shall  subsequently  treat  more  fully  of  friction. 

7* 


78  CRYSTALTZATION— CRYSTALS. 

Crystalization. — If  a  body  pass  from  a  fluid  or  gaseous  form  to 
a  solid  condition,  the  change  is  owing  to  the  preponderance  of  the 
cohesive  force,  which  fixes  the  hitherto  moving  particles  in  a 
relatively  definite  position.  In  this  transition  to  a  solid  condition, 
.we  see  a  tendency  throughout  all  nature  to  produce  a  regular 
arrangement  of  the  molecules,  and  the  force  exercising  this  tend- 
ency in  inorganic  nature  is  crystalization. 

Crystals  are  such  solid  bodies  as  have  a  regular  form  limited  by 
plane  surfaces.  In  nature  we  find  a  number  of  these  crystals : 
for  instance,  quartz,  calcareous  spar,  heavy  spar,  topaz,  garnet, 
&c.,  are  often  found  beautifully  crystalized. 

A  body  almost  always  assumes  the  crystaline  form  on  passing 
from  a  fluid  to  a  solid  condition.  This  transition  is  effected  either 
by  the  cooling  of  a  melted  body,  or  by  separation  from  a  solution. 

If  we  pour  melted  bismuth  into  a  warmed  cup,  a  solid  crust 
will,  after  a  time,  be  formed  upon  the  upper  surface.  If,  now, 
we  puncture  this  crust,  and  pour  off  the  remaining  fluid  metal, 
we  obtain  large  cubic  crystals,  measuring  several  lines  in  length, 
and  filling  up  the  cavity  which  is  formed  by  the  cooled  and  solid 
crust. 

We  may  obtain  crystals  from  a  melted  mass  of  sulphur  in  a 
similar  manner. 

On  attentively  observing  a  portion  of  water  in  the  act  of  freez- 
ing, we  see  delicate  needles  of  ice  forming,  and  every  moment 
spreading  and  ramifying.  It  is  true,  that  we  seldom  see  such 
regular  crystaline  formations  in  ice  as  in  snow,  but  still  it  is  suffi- 
ciently evident,  that  the  formation  of  ice  is  a  process  of  crystali- 
zation. 

Many  bodies  dissolve  in  fluids,  as,  for  instance,  in  water;  but 
only  a  definite  quantity  of  any  substance  will  dissolve  in  a  definite 
quantity  of  water,  although  more  is  generally  dissolved  in  hot 
than  in  cold  water.  If  a  solution  be  saturated  at  a  high  tempera- 
ture, that  is,  if,  for  instance,  as  much  alum  has  been  put  into 
hot  water  as  the  definite  quantity  of  the  liquid  will  dissolve,  the 
whole  mass  of  salt  will  not  remain  wholly  dissolved  on  cooling, 
but  a  portion  will  be  again  deposited,  and  in  the  form  of  regular 
crystals.  Crystals  will  likewise  be  formed  when  the  water  gra- 
dually evaporates  from  a  saturated  solution. 

Crystals  are  not  separated  from  aqueous  solutions  only;  sul- 
phur, for  instance,  dissolves  in  bisulphuret  of  carbon,  chloride  of 


CRYSTALS.  79 

sulphur,  and  oil  of  turpentine ;  and  we  may  obtain  beautiful 
transparent  crystals  of  sulphur  from  these  solutions. 

The  slower  the  cooling  or  evaporation,  the  larger  and  more 
regular  will  the  crystals  be.  In  rapid  crystalization  small  crystals 
are  formed  which  unite  together  in  irregular  groups,  in  which  we 
can  scarcely  recognize  the  crystaline  outline. 

Every  substance  has  its  own  form  of  crystalization.  Thus,  for 
instance,  the  form  of  quartz  is  different  from  that  of  alum,  and 
this  latter  varies  again  from  that  of  sulphate  of  copper  (blue 
vitriol). 

The  investigation  into  the  laws  of  symmetry  which  are  found 
to  enrol  between  the  separate  surfaces  of  crystals,  as  well  as  the 
description  of  crystaline  forms  in  particular,  are  subjects  which 
belong  to  the  province  of  Crystalography. 


80  HYDROSTATICS. 


CHAPTER    III. 

HYDROSTATICS,  OR  THE    THEORY  OF    THE    EQUILIBRIUM    OF  LIQUIDS. 

HYDROSTATICS  treats  of  the  conditions  of  equilibrium  in  liquid 
bodies,  and  of  the  pressure  which  they  exercise  upon  the  walls 
of  the  vessels  in  which  they  are  contained. 

The  properties  of  liquid  bodies  are  dependent  upon  two  forces, 
namely  on  gravity,  which  acts  upon  them  as  upon  all  other  bo- 
dies ;  and  on  molecular  attraction,  the  action  of  which  is  so  modi- 
fied in  them  as  to  give  rise  to  their  liquid  condition.  We  may 
easily  separate  in  our  minds  the  actions  of  these  two  forces,  for 
we  may  form  a  conception  of  a  mass  of  water  devoid  of  weight, 
although  not  ceasing  to  be  fluid. 

Such  a  mass  left  to  itself  would  not  fall ;  it  is  evident  that  to 
be  at  rest  it  neither  requires  to  be  supported  from  below  nor  to  be 
contained  in  any  vessel.  In  this  condition  the  fluid  might  sustain 
and  propagate  a  pressure  according  to  a  law  which  we  will  at 
once  consider. 

Principle  of  the  equality  of  pressure. — Fluids  have  the  property 
of  regularly  propagating  to  all  parts  the  pressure  exercised  upon  a 
portion  of  their  Surface. — This  principle  is  a  physical  axiom ; 
and,  if  it  be  not  necessary  to  prove  it,  we  may  at  any  rate  make 
it  intelligible. 

Fi    53  Let  abed  (Fig.  53)  represent  a  vessel 

containing  a  liquid  supposed  to  be  devoid  of 
weight ;  p  is  a  solid  plate,  completely  cover- 
ing the  upper  surface  of  the  fluid,  which  we 
will  also  suppose  to  be  devoid  of  weight.  If 
the  fluid  is  not  pressed  upon  by  any  weight, 
j~  it  evidently  cannot  suffer  any  pressure,  and 
we  might  bore  the  vessel  at  any  spot  without 
the  fluid  escaping.  But  as  soon  as  we  load  the  plate  with  a 
weight,  say,  for  instance,  100  Ibs.,  it  will  manifest  a  tendency  to 


HYDRAULIC   PRESS.  81 

sink,  and  would  sink  if  the  fluid  did  not  hinder  it  from  so  doing. 
The  fluid,  whether  compressible  or  not,  must  now  support  the  100 
Ibs.  The  upper  surface  x  will,  therefore,  support  the  whole  pres- 
sure, and  would  necessarily  be  pressed  dowr,  if  it  were  not  kept 
up  by  the  layer  y.  The  layer  x  presses  accordingly  upon  the 
layer  y  with  the  same  force  with  which  it  is  pressed  by  the  plate. 
Thus  the  layer  y  presses  upon  the  next  one  z,  and  in  the  same 
manner  the  pressure  is  conveyed  to  the  bottom,  which  is  itself 
pressed  upon,  as  if  the  plate  rested  immediately  upon  it.  As  now 
the  whole  bottom  sustains  a  pressure  of  one  hundred  pounds,  it  is 
evident  that  the  half  of  the  surface  of  the  bottom  will  bear  only 
a  weight  of  fifty  pounds,  and  the  hundredth  part  of  the  same  sur- 
face only  one  pound.  Hence  it  follows: — 

1.  That  the  pressure  is  communicated  from  above  downward  to 
horizontal  surfaces  without  diminution. 

2.  That  it  is  equal  at  all  points. 

3.  That  it  is  proportionate  to  the  extension  of  the  surfaces  con- 
sidered. 

The  same  occurs  with  regard  to  the  lateral  surfaces.  If  we 
were  to  make  an  opening  in  the  lateral  wall,  the  liquid  would 
gush  forth;  and  if  we  were  to  cut  out  of  the  wall  a  piece,  the 
surface  of  which  should  equal  that  of  the  plate,  we  must  have  a 
counter  pressure  of  one  hundred  pounds.  If  the  plate  itself  had 
an  opening,  the  water  would  gush  forth  from  it,  by  which  it  is 
evident  that  the  under  surface  of  the  plate  is  pressed  upon,  exactly 
the  same  as  all  the  other  portions  of  the  walls.  Fluids,  therefore, 
communicate  a  pressure,  exercised  upon  any  part  of  their  upper 
surface,  equally  in  all  directions.  If  we  once  understand  this 
principle  with  regard  to  fluids  devoid  of  weight,  it  can  easily  be 
applied  to  heavy  fluids  on  each  molecule  of  which,  a  pressure  is 
exercised,  arising  from  their  own  proper  gravity. 

The  Hydraulic  Press  depends  upon  the  uniform  communication 
of  pressure  by  fluids,  and  consists  of  two  main  parts,  a  sucking 
and  forcing  pump,  which  exercise  the  pressure,  and  a  piston  with 
a  plate  to  receive  the  pressure,  and  convey  it  to  the  bodies  to  be 
pressed. 

Fig.  54  is  a  section,  and  Fig.  55  a  complete  representation  on 
a  small  scale  of  the  hydraulic  press.  The  piston  s  is  raised  by 
the  lever  /,  and  the  water  of  the  reservoir  b  pressing  through  the 
perforated  vessel  r  lifts  the  valve  i,  and  thus  gets  beneath  the 


82 


HYDRAULIC    PRESS. 


piston  s.  If  we  press  down  the  lever  J,  the  piston  5  goes  down, 
the  water  is  forced  back,  closes  the  valve  i,  raises  the  valve  d,  and 
runs  through  the  tube  t  b  u  into  the  cylinder  c  c'  of  the  press : 

Fig.  54. 


Fig.  55. 


here  it  presses  against  the  piston  p,  which  it  lifts  with  the  plate  p'9 
and  thus  the  body  to  be  acted  on  is  compressed  between  pf  and 
the  fixed  plate  e. 

The  efficiency  of  the  hydraulic  press  rests  upon  the  principle 
that  fluids  communicate  every  pressure  equally  in  all  directions. 
If  the  piston  s  be  pressed  down  by  any  force,  each  portion  of  the 


EQUILIBRIUM   OF   HEAVY   FLUIDS.  83 

surface  of  the  walls  of  the  vessel,  which  is  equal  to  the  diagonal 
section  of  the  piston,  has  to  sustain  an  equal  pressure.  But  now 
we  may  regard  the  under  surface  of  the  piston  p  as  a  part  of  the 
wall  of  the  vessel ;  therefore,  as  many  times  as  the  diagonal  sec- 
tion of  the  piston  p  is  greater  than  the  diagonal  section  of  the 
piston  5,  so  many  times  will  the  force  with  which  the  piston  p  is 
elevated  be  greater  than  the  force  with  which  the  small  piston  is 
depressed. 

If  the  area  of  a  section  of  the  piston  s  is  r^oth  of  the  area  of 
the  piston  p,  then  p  will  be  elevated  with  a  force  of  100  pounds,  if 
s  is  pressed  by  a  force  of  one  pound.  But  with  the  help  of  the 
lever  /,  a  man  may  easily  exercise  a  pressure  of  300  pounds  on 
the  piston  s,  and  therefore  raise  the  piston  p  with  a  force  of 
30,000  pounds. 

A  portion  of  the  force  applied  to  the  lever  /  is  lost  by  the  resist- 
ance of  friction  before  it  is  transmitted  to  the  piston  p :  the  effect, 
therefore,  will  always  be  less  than  what  it  should  be  according  to 
the  above  considerations. 

Equilibrium  of  heavy  Fluids. — Two  conditions  must  be  fulfilled 
in  order  that  liquid  bodies  should  be  in  equilibrium.  First,  their 
free  surfaces  must  be  at  right  angles  with  the  direction  of  gravity ; 
and  secondly,  the  forces  of  pressure  acting  on  each  particle  must 
always  be  equal  and  opposed,  the  one  to  the  other. 

If  we  assume  that  the  upper  surface  of  the  fluid  is  not  at  right 
angles  with  the  direction  of  gravity,  but  takes  such  a  form  as  a  b 
e  d  (Fig.  56),  we  may  suppose  an  inclined 
plane  laid  through  any  two  points,  b  and  e;  a.  Flg' 56> 

portion  of  the  fluid  lies  on  this  inclined  plane, 
and  must  necessarily  glide  off  from  the  easy 
displacement  of  the  particles.  This  will  con- 
tinue until  the  whole  upper  surface  is  every- 
where at  right  angles  with  the  direction  of 
gravity. 

If  we  apply  this  to  the  upper  surface  of  the 
sea,  which  we  will  consider  as  perfectly  at  rest,  it  is  clear  that  if 
the  force  of  gravity  alone  acts,  and  is  always  directed  towards  the 
central  point  of  the  earth,  the  superficies  of  all  seas  must  be  por- 
tions of  a  spherical  surface,  and  that,  therefore,  the  surfaces  of 
seas  connected  together  must  be  equally  remote  from  this  central 
point. 


84  PRESSURE    OF    FLUIDS. 

If  the  molecules  are  attracted  by  other  forces  than  terrestrial 
gravity,  we  may  easily  understand  that  their  free  surfaces  must  be 
at  right  angles  to  the  resultant  of  gravity,  and  all  the  other  simul- 
taneously acting  forces.  As  the  centrifugal  force,  which  depends 
on  the  rotatory  movement  of  the  earth,  continually  acts  with 
gravity  upon  all  bodies,  the  upper  surface  of  the  waters  must 
assume  such  a  position  as  to  be  at  right  angles  with  the  resultant 
of  both  forces.  This  is  also  the  reason  that  the  sea  is  flattened 
at  the  poles.  At  the  foot  of  great  mountains  which  cause  the 
plummet  to  diverge,  the  surface  of  the  water  also  deviates  from 
the  regular  form.  In  the  same  way  the  attractive  force  of  the 
moon,  which  acts  upon  the  water,  combines  with  gravity  to  create 
a  resultant  which  is  not  vertical.  The  moving  surface  of  the 
sea  always  strives  to  attain  to  a  position  of  equilibrium,  which  is 
constantly  disturbed  by  the  motion  of  the  moon,  and  hence  the 
periodical  oscillations  of  ebb  and  flow. 

We  also  observe  deviations  from  the  normal  surface  in  fluids 
enclosed  in  vessels  ;  thus  water  in  a  glass  is  not  even  over  its 
whole  surface,  but  rises  around  the  margin;  the  surface  of 
mercury,  on  the  contrary,  is  depressed  at  the  sides,  as  if  it  dreaded 
coming  in  contact  with  the  walls  of  the  vessel.  These  pheno- 
mena depend  upon  the  laws  of  capillary  attraction,  which  we 
purpose,  subsequently,  to  consider  more  fully. 

The  second  condition  of  equilibrium  is  self-evident,  for  the 
molecules  that  are  in  the  interior  of  the  fluid  sustain  a  pressure 
from  all  the  other  molecules  lying  over  them,  which  they  transmit 
in  all  directions.  But  if  the  various  pressures,  acting  in  different 
directions  upon  one  molecule,  were  not  equal,  it  would  be  dis- 
placed by  the  strongest  pressure,  and  consequeutly  the  fluid  mass 
would  not  be  in  equilibrium. 

Pressure  of  Fluids. — If  fluid  masses  are  in  a  state  of  equili- 
brium, they  exercise  upon  themselves  and  on  all  solid  bodies 
which  they  touch,  a  more  or  less  considerable  pressure,  the  amount 
of  which  we  will  now  determine.  In  the  first  place  we  will  exa- 
mine the  pressure  exercised  from  above  downwards,  or  from  be- 
low upwards,  on  horizontal  surfaces,  and  then  the  pressure  acting 
upon  the  lateral  surfaces. 

The  pressure  exercised  by  a  fluid  from  above  downward  on  the 
bottom  of  the  vessel  in  which  it  is  contained  is  quite  independent 
of  the  form  of  the  vessel,  and  is  always  equal  to  the  weight  of  a 


PRESSURE    OF   FLUIDS.  85 

column  of  the  fluid,  whose  base  is  the  bottom  of  the  vessel,  and 
whose  height  is  the  vertical  distance  from  the  bottom  to  the  sur- 
face of  the  fluid. 

The  first  part  of  this  assertion  is  easily  proved  by  help  of  the 
following  apparatus : — The  apparatus  (Fig.  57)  consists  of  a  bent 
tube,  a  b  c  fastened  in  a  box,  and  so  arranged  that  vessels  of 
different  form,  as  those  at  d  ef  g  (Figs.  58,  59  and  60),  may  be 
screwed  on  at  a.  We  pour  mercury  into  the  tube,  and  with  the 

Fig.  57.  Fig.  58.  Fig.  59.         Fig.  60. 


help  of  a  moving  index  indicate 
the  height  n  to  which  the  mer- 
cury rises  in  the  arm  c.     If  now 
the  cylindrical  vessel  d  be  screwed  on  at  a,  and  filled  with  water 
to  a  definite  height  A,  the  mercury  will  rise  in  the  tube  c  to  a 
height  p,  which  we  must  mark.     The  rising  of  the  mercury  n  p 
evidently  depends  upon  the  pressure  exercised  by  the  water  in  the 
vessel  d  upon  the  surface  of  mercury  which  forms  the  true  bottom 
of  the  vessel.     When  this  has  been  duly  observed,  we  empty  the 
vessel  d  by  the  help  of  the  cock  r,  and  screw  on  in  its  place  either 
the  vessel  e,  widened  at  its  upper  margin,  or  /,  tapering  off 
towards  the  top.     If  we  fill  these  vessels  with  water,  as  high  as 
we  before  did  the  vessel  d,  the  mercury  in  the  tube  c  will  again 
rise  exactly  to  the  height  p.     The  pressure,  therefore,  which  the 
bottom  of  these  three  differently  shaped  vessels  bears,  is  precisely 
the  same,  if  only  the  height  of  the  fluid  be  the  same.     The  pres- 
sure on  the  bottom  is,  therefore,  as  we  before  observed,  inde- 
pendent of  the  form  of  the  vessel,  and  only  depends  upon  the  size 
of  the  bottom,  the  height  and  nature  of  the  fluid.     The  pressure 
is  the  same,  whether  the  vessel  be  cylindrical,  contain  much 
(Fig.  61)  or  little  (Fig.  62)  fluid,  be  rectangular  (Fig.  63)  or 
inclined  (Fig.  64).     In  order  to  prove  the  second  part  of  the  pro- 
8 


86  PRESSURE    OF    FLUIDS. 

position,  it  will  suffice  to  remark,  that  the  bottom  of  the  cylin- 
drical vessel  (Fig.  62)  must  bear  the  whole  weight  of  the  fluid, 


Fig.  61.  Fig.  62.  Fig.  63.  Fig.  64. 


or,  as  the  lateral  walls  are  vertical,  they  are  incapable  of  sup- 
porting the  least  part  of  the  weight  of  the  fluid.  As,  now,  the 
bottoms  of  the  inclined  vessels,  whether  they  are  widened  or  con- 
tracted at  their  upper  margin,  sustain  the  same  weight,  it  follows 
that  in  these  vessels  the  pressure  is  no  longer  equal  to  the  weight 
of  the  fluid  they  contain,  but  is  equal  to  the  weight  of  a  straight 
column  of  water  having  the  same  surface  and  height.  As  all 
parts  of  the  bottom  are  pressed  upon  with  equal  force,  it  is  clear 
that  the  half,  the  third,  fourth  part,  &c.,  must  sustain  J,  J,  J  of 
the  whole  pressure.  If  we  designate  by  g  the  portion  of  the 
bottom  we  are  considering,  by  h  the  height  of  the  smooth  surface, 
and  by  d  the  density  of  the  fluid,  the  pressure  upon  the  surface  s 
is  equal  to  s  X  h  X  rf,  for  s  X  h  is  the  volume  of  the  straight 
column  of  fluid,  and  in  order  to  obtain  the  weight  we  must  mul- 
tiply the  volume  by  the  density. 

With  a  litre*  of  water  weighing  a  kilogramme,!  we  may  there- 
fore exercise  a  very  small,  or  any  unlimitably  large  amount  of 
pressure  upon  the  bottom  of  a  vessel.  If  the  pressure  upon  the 
bottom  is  to  be  exactly  one  kilogramme,  we  must  take  a  straight 
cylindrical  vessel  of  any  base  we  choose,  when  the  combined 
pressure  upon  the  whole  surface  will  always  be  one  kilogramme ; 
only  the  pressure  which  each  square  centimetre  of  the  bottom  has 
to  sustain  will  be  large  or  smaller,  as  the  vessel  is  wider  or 
narrower. 

If  we  would  exercise  upon  the  bottom  of  the  vessel  a  pressure 
of  ro  of  a  kilogramme  with  one  kilogramme  of  water,  we  might 
take,  for  instance,  a  vessel  whose  bottom  should  measure  a  square 


*  The  litre  is  equal  to  2.113  pints,  or  nearly  equal  to  the  English  quart, 
f  The  kilogramme  is  equal  to  15,444  grains,  or  rather  more  than  two  pounds 
avoirdupois  (2.2.  4.  16). 


PRESSURE   OF   FLUIDS. 


87 


decimetre,  and  which  was  so  widened  towards  the  top,  that  a  litre 
of  water  would  only  fill  it  to  the  height  of  one  centimetre. 

If  the  pressure  was  to  amount  to  ten  kilogrammes,  we  might 
take  a  vessel  of  the  same  base  (one  square  decimetre)  so  narrowed 
towards  the  top,  that  a  litre  of  water  would  rise  in  it  to  the  height 
of  ten  decimetres. 

With  a  similar  weight  of  one  kilogramme  of  water,  we  might 
with  equal  ease  exercise  a  pressure  of  7^,  yoW,  &c.  part  of  a  kilo- 
gramme, as  one  of  100,  1000,  &c.  kilogrammes.  The  pressure 
of  fluids  acts  not  only  on  the  bottom  of  the  vessel,  but  upon  every 
point  in  the  interior  of  the  fluid  mass.  If  we  assume  in  the  interior 
of  a  fluid  mass  a  stratum  m  p  parallel  with  the 
surface,  all  the  molecules  of  this  stratum  will 
evidently  be  pressed  upon  by  the  fluid  over  it, 
bearing  the  weight  of  the  fluid  cylinder  n  v  m  p. 
The  stratum  must,  however,  sustain  an  equal 
pressure  in  an  opposite  direction  from  below  up- 
wards. If  now  we  consider  a  part  a  b  of  the  said 


Fig.  65. 


Fig.  66. 


stratum,  we  find  that  the  weight  of  the  fluid  column  abed  presses 
upon  it  from  above  downwards,  while  an  equal  force  acts  from 
below  upwards.  If,  therefore,  we  immerse  a  solid  cylinder  in  the 
fluid,  its  base  will  have  to  support  a  pressure  from  below  which 
strives  to  raise  it. 

This  may  be  proved  by  the  following  experiment: — Take  a 
somewhat  wide  glass  tube  v  (Fig.  66), 
whose  lower  margin  has  been  smoothly 
polished :  t  is  a  perfectly  smooth  glass  disc, 
secured  in  its  centre  by  a  thread  passing 
through  the  tube,  so  that  by  drawing  the 
thread,  the  disc  may  be  made  entirely  to 
close  the  opening  of  the  tube.  When 
secured  in  this  manner,  we  immerse  the 
tube  in  the  water.  Now,  it  is  no  longer 
necessary  to  draw  the  thread  in  order  to 
prevent  the  falling  of  the  disc,  for  it  is  pressed  upwards  by  the 
fluid.  If  we  pour  water  into  the  tube,  the  glass  disc  will  fall  by 
its  own  weight  as  soon  as  the  level  of  the  water  in  the  tube  is 
almost  equal  to  that  of  the  water  in  which  it  is  immersed,  for 
now  the  glass  disc  sustains  equal  fluid  pressure  upwards  and 
downwards. 


88  PRESSURE    OF    FLUIDS. 

If,  accordingly,  we  were  to  make  an  opening  in  a  ship,  the 
water  would  instantly  enter  the  vessel :  we  must,  in  order  to  hinder 
this,  exercise  a  counter  pressure  equal  to  the  weight  of  a  column 
of  water,  having  the  same  base  as  the  opening,  and  of  the  same 
height  as  the  depth  of  the  opening  below  the  level  of  the  water. 
The  bottoms  of  large  ships  must,  therefore,  be  very  strongly  built 
to  sustain  the  pressure  of  the  water  from  below  upwards.  If  we 
assume  that  the  bottom  is  horizontal,  and  has  a  superficies  of 
100  square  metres  (about  119  square  yds.),  this  pressure  would 
amount  to  100,000  kilogrammes  (214,500  Ibs.)  if  it  were  one 
(1  yd.  3  in.),  and  300,000  kilogrammes  (643,500  Ibs.)  if  it  were 
three  metres  (3  yds.  9  in.)  below  the  level  of  the  sea. 

We  may  thus  form  an  idea  of  the  enormous  pressure  sustained 
by  the  living  creatures  inhabiting  the  depths  of  the  seas  and 
oceans.  We  shall  again  revert  to  this  subject. 

The  pressure  which  a  given  portion  of  lateral  wall  has  to  sup- 
port, is  equal  to  the  weight  of  a  column  of  fluid  whose  height  is 
equal  to  the  depth  of  the  centre  of  gravity  of  this  lateral  wall 
below  the  level  of  the  fluid,  and  whose  horizontal  base  is  equal  to 
the  size  of  the  given  portion  of  the  wall. 

The  amount  of  lateral  pressure  may  be  obtained  from  the  cor- 
responding horizontal  pressure,  according  to  the  principle  of  the 
uniform  transmission  of  pressure  in  all  directions.  The  point  m 
(Fig.  65)  is  a  point  in  the  horizontal  layer  m  p;  the  pressure  to 
which  it  is  exposed  transmits  itself  uniformly  in  all  directions, 
therefore,  also  at  right  angles  to  the  wall.  Every  point  of  the 
lateral  wall  sustains,  therefore,  the  same  pressure  as  every  point 
of  the  equally  high  horizontal  stratum  of  fluid.  If,  now,  we  con- 
sider any  portion  of  the  area  of  the  lateral  wall,  whose  highest 
point  is  so  little  elevated  above  the  lowest  point  that  the  pressure 
sustained  by  both  may,  without  any  great  error,  be  assumed  as 
equal,  then  we  find  that  the  pressure  sustained  by  this  portion  of 
the  area  is  s  X  h  X  d,  if  s,  h  and  d  have  the  previously  assumed 
significations.  In  a  vat  full  of  water,  ten  metres  (10  yds.  2  ft. 
9  in.)  in  height,  the  pressure  upon  a  square  centimetre  of  the 
lateral  wall  at  the  depth  of  one  metre  (1  yd.  3  in.)  is  equal  to  100 
grammes  (3  oz.  6  drs.  12  grs.);  and  at  two  metres  (2  yds.  6  in.) 
to  200  grammes  (6  oz.  12  drs.  24  grs.);  and  at  ten  metres,  that 
is  at  the  bottom,  to  one  kilogramme  (2  Ibs.  2  oz.  4  drs.  16  grs.). 

The  pressure  sustained  by  any  point  of  the  vertical  wall  of  a 


COMMUNICATING   VESSELS. 


89 


Fig.  67. 


vessel  filled  with  water  may  be  made  manifest  by  a  diagram  (Fig. 
67).  From  a  let  a  straight  line  be 
drawn  a  b,  equal  in  length  to  the  depth 
of  the  point  a  below  the  level  of  the 
water,  a  b  will  then  represent  the  pres- 
sure which  the  point  has  to  sustain. 
If  we  make  the  same  figure  for  several 
points  of  the  vertical  line  r  s,  the  ex- 
tremities of  all  the  horizontal  lines  of 
pressure  will  fall  upon  the  line  r  t.  It  follows,  therefore,  that  the 
combined  pressure  which  the  line  r  s  of  the  vertical  wall  of  the 
vessel  has  to  sustain,  is  represented  by  the  triangle  r  s  t.  The 
point  of  application  of  the  resultant  of  all  the  elementary  pres- 
sures sustained  by  a  section  of  a  wall  is  called  the  centre  of 
pressure.  It  always  lies  deeper  than  the  centre  of  gravity  of  the 
section,  because  the  pressure  increases  in  intensity  downwards. 
The  centre  of  pressure  for  the  vertical  line  r  s  is  easily  obtained, 
for  it  is  evidently  the  point  c  at  wrhich  the  line  r  s  is  intersected  by 
the  horizontal  line  passing  through  the  centre  of  gravity  o  of  the 
triangle  r  s  t.  We  have  here  only  considered  a  line  r  s;  but,  if 
for  this  we  substitute  a  broad  band  of  the  vertical  wall,  its  centre 
of  pressure  will  lie  upon  its  vertical  central  line,  and  its  height 
above  the  bottom  will  be  one-third  of  the  height  of  the  level  of 
the  water  above  the  bottom. 

Communicating  vessels.  —  The  above  developed  conditions  of 
equilibrium  are  valid  equally  for  fluids  contained  in  vessels  that 
are  connected  together;  that  is  to  say,  if  both  vessels  contain  the 
same  fluid,  the  level  must  be  the  same  in  both.  If  we  assume  a 
horizontal  partition  wall  to  be  applied  at  m  to  the  vessel  (Fig.  68), 


Fig.  68. 


Fig.  69. 


we  obtain  two  vessels. 
According  to  the  princi- 
ples advanced,  the  pres- 
sure which  this  partition 
wall  sustains  from  below 
is  jB  A,  if  B  designate 
the  area  of  the  partition, 
and  h  the  height  p  v.  If  a  b  is  the  level  of  the  fluid  in  the  wider 
vessel,  and  h'  represent  the  height  a  m,  then  the  pressure  which 
the  partition  wall  has  to  support  from  above  downwards  is  B  h'. 
If,  now,  we  suppose  the  partition  wall  again  removed,  the  layer 

8* 


90  COMMUNICATING   VESSELS. 

of  water  taking  its  place  will  have  to  sustain  on  the  one  side  the 
pressure  B  h,  and  on  the  other  the  pressure  B  h'.  Motion  will 
necessarily  occur  as  soon  as  h  is  not  equal  to  h' .  There  can, 
therefore,  only  be  equilibrium  when  h  and  h'  are  actually  equal ; 
that  is,  when  the  level  of  the  fluid  is  equally  high  in  both  vessels. 
If  the  fluids  in  the  two  vessels  are  dissimilar,  the  level  will  not  be 
equally  high  in  both. 

In  the  tube,  for  instance,  (Fig.  70,)  there  is  water  in  one 
side,  and  in  the  other  mercury,  the  fluids  meet- 
ing at  g.  Below  the  horizontal  plane  passing 
through  g  there  is  only  mercury,  which  is  per- 
fectly in  equilibrium.  The  column  of  mercury 
over  h  has,  therefore,  to  keep  in  equilibrium  the 
column  of  water  above  g,  and,  that  this  may 
happen,  the  heights  of  the  columns  must  be 
inversely  to  each  other  as  the  specific  gravities 
of  the  fluids ;  that  is  to  say,  the  column  of  water  must  be  nearly 
fourteen  times  as  high  as  the  column  of  mercury,  because  the 
specific  gravity  of  water  is  nearly  fourteen  times  less  than  that  of 
mercury. 

Whatever  be  the  fluids  used,  the  heights  of  the  columns  must 
always  bear  an  inverse  ratio  to  their  specific  gravities.  Thus  a 
column  eight  inches  high  of  concentrated  sulphuric  acid  will 
equipoise  one  of  water  14.8  inches  high;  and  a  column  eight 
inches  high  of  sulphuric  ether  will  be  in  equilibrium  with  a 
column  of  water  5.7  inches  high. 

We  often  see  that  heavy  bodies  move  in  an  opposite  way  to 
the  direction  of  gravity ;  cork  and  wood,  for  instance,  rise  on  the 
surface  when  they  are  immersed  in  water;  in  the  same  manner 
iron  rises  in  mercury,  and  the  air  balloon  in  the  air.  All  these 
phenomena  depend  upon  the  principle  known  by  the  name  of 
the  Archimedean  principle,  from  having  been  discovered  by 
Archimedes. 

This  principle  may  be  thus  expressed: — Jl  body  immersed  in  a 
fluid  loses  a  portion  of  its  weight  exactly  corresponding  with  the 
weight  of  the  fluid  displaced  by  it.  Or,  to  express  the  same  more 
correctly :— If  a  body  be  immersed  in  a  fluid,  a  portion  of  its 
weight  will  be  sustained  by  the  fluid,  equal  to  the  weight  of  the 
fluid  displaced. 

WTe  may  convince  ourselves  of  the  truth  of  this  principle  by 


COMMUNICATING   VESSELS. 


91 


Fig.  71. 


means  of  a  simple  experiment.  Immerse  a  regular  prism  verti- 
cally in  a  fluid,  as  shown  at  Fig.  71,  then  every  pressure  on  the 
sides  of  the  prism  is  destroyed  by  an  equal  and 
opposite  pressure ;  but  the  upper  surface  sustains 
the  pressure  of  a  column  of  fluid  having  an  equal 
base  with  the  prism,  and  the  height  h.  The  under 
surface,  however,  is  pressed  upon  from  below  up- 
wards by  a  force  equal  to  the  weight  of  a  column 
of  fluid  of  the  same  base,  and  of  the  height  h'. 
The  heights  h  and  h'  differ  exactly  by  the  height  of  the  prism, 
and  therefore  it  is  clear  that  the  pressure  on  the  under  surface 
exceeds  that  on  the  upper  surface  by  the  weight  of  a  column  of 
fluid  equal  to  the  volume  of  the  prism.  But,  as  this  excess  of 
pressure  acts  upwards  against  the  gravity  of  the  body,  the  action 
of  the  force  of  gravity  of  the  body  is  evidently  diminished  in  the 
way  specified.  If,  for  instance,  the  base  of  this  prism  be  one 
square  centimetre,  its  height  ten  centimetres,  and  the  upper 
surface  three  centimetres  below  the  level  of  the  water,  the  upper 
has  to  sustain  a  pressure  of  a  column  of  water  whose  base  is  one 
square  centimetre,  its  height  three  centimetres ;  consequently  a 
weight  of  three  cubic  centimetres  of  water,  that  is,  of  three 
grammes.  But  the  lower  surface  is  thirteen  centimetres  below 
the  level  of  the  water,  and  has,  therefore,  to  sustain  a  force  acting 
from  below  upwards  and  equal  to  the  weight  of  a  column  of  water 
whose  base  is  one  square  centimetre  and  height  thirteen  centi- 
metres, that  is,  thirteen  grammes.  If  we  deduct  from  these  thir- 
teen grammes  the  amount  of  the  pressure  of  the  three  grammes 
acting  downwards  upon  the  upper  surface,  there  remain  ten 
grammes  for  the  force  with  which  the  prism  is  urged  'upwards 
by  the  pressure  of  the  water.  But  ten  grammes  is  the  weight  of 
a  column  of  water  of  equal  volume  with  the  prism.  If  this  prism 
were  of  marble,  it  would  weigh  twenty-seven  grammes ;  but,  on 
being  immersed  in  water,  it  has  to  sustain  a  pres- 
sure of  ten  grammes  directed  upwards,  and,  con- 
sequently, in  the  water  it  will  be  ten  grammes 
lighter.  If,  in  the  place  of  one  prism,  we  take 
several  together,  it  is  clear  that  each  separate  one 
will  lose  on  being  immersed  in  the  water  an  amount 
of  weight  equal  to  an  equal  volume  of  water,  and, 
consequently,  the  loss  of  weight  sustained  by  the 


Fig.  72. 


92 


THE    BALANCE. 


whole  body  composed  of  the  several  prisms  will  equal  the  weight 
of  a  mass  of  water  of  equal  volume  to  the  combined  volume  of 
the  prisms.  As,  however,  we  may  imagine  any  body  decom- 
posable into  a  number  of  such  vertically-placed  prisms  of  very 
small  diameter,  the  conclusion  may  be  extended  to  any  body  we 
choose  to  take. 

A  totally  different  mode  of  deduction  leads  us  to  the  same 
result.  If  we  suppose  the  space  occupied  by  the  body  immersed 
in  water  to  be  filled  with  water,  this  body  of  water  will  float  in 
the  remaining  mass  of  the  liquid,  neither  rising  nor  sinking.  If, 
now,  we  assume  this  body  of  water  to  be  replaced  by  another 
which,  with  an  equal  volume,  has  also  an  equal  weight,  this  latter 
will  likewise  float,  its  whole  weight  being  sustained  by  the  water 
in  which  it  is  immersed,  whence  it  is  clear  that  a  portion  of  the 
weight  of  every  immersed  body  is  sustained  by  the  water,  and  is 
equal  to  the  weight  of  the  fluid  displaced. 

We  may  convince  ourselves  of  the  truth  of  the  Archimedean 
principle  by  direct  experiment.  To  one  of  the  scale-pans  of 
an  ordinary  balance  (Fig.  73)  is  attached  a  hollow  cylinder,  c, 

Fig.  73. 


from  which  is  suspended  a  massive  cylinder,  p,  accurately  filling 
the  cavity"  of  the  former.  On  the  other  scale-pan  are  placed 
sufficient  weights  d,  to  equipoise  the  whole.  If,  now,  the  cylinder 
p  be  immersed  in  water,  it  will  lose  a  portion  of  its  weight,  and 
the  equilibrium  will  be  thus  disturbed ;  to  re-establish  this,  the 
cylinder  c  need  only  be  filled  with  water,  which  clearly  proves 


SUBMERGED    BODIES.  93 

that  p  has  lost  as  much  weight  by  being  immersed  in  the  water 
as  the  contents  of  the  cylinder  c  weigh.  But  the  volume  of  water 
in  c  is  equal  to  the  water  displaced  by  the  cylinder^?,  and  the  loss 
of  weight  of  p  is  consequently  equal  to  the  weight  of  the  displaced 
water. 

As  we  have  already  seen,  there  would  be  equilibrium  if  we 
could  convert  into  water  the  immersed  body.  But  this  body  of 
water  would  remain  perfectly  in  equilibrium,  whichever  way  it 
were  turned,  round  its  centre  of  gravity.  The  pressure  of  the 
surrounding  fluid  acting  from  below  upwards  is,  therefore,  a  force 
whose  point  of  application  corresponds  with  the  centre  of  gravity 
of  the  ideal  body  of  water.  This  point  may  be  termed  the  centre 
of  pressure  of  the  fluid. 

If,  now,  this  ideal  body  of  water  be  replaced  by  any  other 
substance,  as,  for  instance,  cork,  marble,  or  iron,  the  pressure 
which  this  body  will  have  to  sustain  from  the  surrounding  mass 
of  water  will  be  precisely  the  same  as  that  which  the  ideal  body 
of  water  has  supported.  A  body  immersed  in  water  is,  therefore, 
subject  to  the  action  of  two  forces,  whose  magnitude  and  point 
of  application  we  now  know.  The  first  force  is  the  gravity  of  the 
body  acting  from  above  downwards,  and  whose  point  of  applica- 
tion is  the  centre  of  gravity  of  the  body ;  the  second  force  acting 
from  below  upwards  is  equal  to  the  weight  of  the  water  displaced, 
and  its  point  of  application  is  the  centre  of  gravity  of  this  mass  of 
water.  If  an  entirely  submerged  body  is  perfectly  homogeneous, 
its  centre  of  gravity  will  correspond  with  the  centre  of  gravity  of 
the  water  displaced. 

This  upward  pressure  of  fluids  is  designated  by  the  term  buoy- 
ancy. 

Conditions  of  equilibrium  of  submerged  Bodies. — For  a  perfectly 
homogeneous  body  submerged  in  water  to  keep  itself  suspended, 
nothing  more  is  necessary  than  that  its  weight  be  exactly  equal  to 
that  of  the  fluid  displaced,  the  position  of  the  body  being  entirely 
indifferent :  here  we  have  an  instance  of  indifferent  equilibrium. 
In  order  to  prove  this  by  an  experiment,  let  us  form  a  body  of  any 
shape  from  a  mass  composed  of  one  part  of  finely  pulverized 
cinnabar,  and  226  parts  of  white  wax.  The  constituents  must 
be  well  worked  together,  that  the  mass  may  have  the  requisite 
uniformity.  A  body  thus  composed  will  float  in  water,  and  re- 
main in  equilibrium  in  any  position  in  which  we  place  it.  In 


94  FLOATING    BODIES. 

spirits  of  wine  it  will  sink,  while  on  a  saline  solution  it  will  rise 
and  float  on  the  surface. 

If  the  immersed  body  be  not  homogeneous,  so  that  its  centre 
of  gravity  does  not  correspond  with  the  centre  of  gravity  of  the 
water  displaced,  it  may  still  float  in  the  fluid,  if  its  total  weight  is 
exactly  equal  to  the  weight  of  the  water  displaced ;  but  it  can  only 
be  in  equilibrium  if  the  centre  of  gravity  of  the  body  and  that  of 
the  water  displaced  be  in  a  vertical  line,  and  stable  equilibrium 
can  only  be  established  if  the  centre  of  gravity  of  the  body  is  in 
the  lowest  position. 

Conditions  of  equilibrium  of  Floating  Bodies. — If  a  body  float, 
its  whole  weight  is  equal  to  the  weight  of  fluid  mass  displaced  by 
the  immersed  portion  of  the  body :  the  condition  of  the  stability  of 
floating  bodies  differs,  however,  from  that  of  submerged  bodies. 
A  ship,  for  instance,  weighing  one  million  kilogrammes  is  in 
equilibrium  if  it  displace  1000  cubic  centimetres  of  water ;  and, 
if  its  centre  of  gravity  and  the  centre  of  pressure  of  the  water  lie 
in  a  vertical  line,  we  may  have  a  condition  of  stability  even  if 
the  centre  of  gravity  do  not  lie  below  the  centre  of  pressure,  it 
being  sufficient  if  it  lie  lower  than  another  point,  termed  the  meta- 
centre.  The  position  of  this  latter  point  depends  upon  the  form 
of  the  ship,  and  the  position  of  the  centre  of  gravity  upon  the 
manner  in  which  the  ship  is  loaded. 

Although  a  general  determination  of  the  metacentre  would  be 

hardly  in  place  here,  we  must  yet  endeavor  to  give  some  idea  of 

it: — Let  abed  (Fig.  74)  be  the  section  of  an  immersed  body, 

and,  for  the  sake  of  clearer  illustration,  let  us  assume  this  section 

to  be  an  elongated  parallelogram.    If  the 

Fig.  74.  ,  .       .  &  .  .  .,.,    . 

body  swim  in  a  position  ot  equilibrium, 
it  will  sink  as  low  as  ef.  The  centre  of 
gravity  of  the  displaced  mass  of  water  is 
at  m,  and  the  centre  of  gravity  of  the 
body  lies  upon  the  vertical  line,  passing 
through  m.  If  it  be  below  m,  the  body 
will  swim  stably  in  every  case,  for  we 
have  a  body  suspended,  as  it  were,  at  the  point  m  in  the  water, 
and  whose  centre  of  gravity  is  deeper  than  its  point  of  suspension, 
and  consequently  a  pendulum  that  oscillates  about  the  position  of 
equilibrium. 

If  the  body  be  changed  from  the  position  of  equilibrium  to  the 


HYDROSTATIC    BALANCE.  95 

one  represented  in  Fig.  75,  the  triangle  e  g  h  is  raised  out  of  the 
water,  while  g  If  is,  on  the  contrary, 
immersed ;  but,  as  the  quantity  of  the 
water  displaced  must  always  be  the 
same,  whatever  be  the  position  of  the 
body,  it  follows  that  e  g  h  =  g  if. 
But  the  form  of  the  submerged  por- 
tion differs  from  what  it  previously 
was,  and,  consequently,  the  centre  of 
gravity  of  the  displaced  mass  of  water  is  no  longer  at  m,  but  at 
another  point  o,  whose  position  must  be  especially  ascertained  in 
each  individual  case.  If  we  suppose  a  perpendicular  drawn 
through  o,  it  will  intersect  at  a  point  g  the  perpendicular  drawn 
in  the  position  of  equilibrium  through  m;  the  point  q  is  the  meta- 
centre.  When  the  centre  of  gravity  of  the  body  lies  below  y,  on 
the  line  m  q,  the  weight  of  the  body  acting  at  o  will  turn  it  round 
o  in  such  a  manner  as  to  make  it  return  to  a  position  of  equili- 
brium. A  floating  body  loses  its  stability  entirely  if  its  centre  of 
gravity  lie  above  the  metacentre. 

The  broader  the  immersed  portion,  and  the  lower  its  centre  of 
gravity,  the  greater  is  the  stability  of  a  floating  body. 

The  Archimedean  principle  affords  us  excellent  means  of  ascer- 
taining the  weight  of  solid  and  fluid  bodies.  In  order  to  compute 
the  density  of  a  solid  body,  we  must  know  its  absolute  weight, 
and  the  weight  of  an  equal  volume  of  water.  But  in  most  cases 
it  is  very  difficult,  and  even  impossible,  to  obtain  the  volume  of  a 
body  by  measuring  its  dimensions.  According  to  the  Archime- 
dean principle,  a  single  experiment  gives  us  without  anything  fur- 
ther being  necessary,  the  weight  of  a  mass  of  water,  having  an 
equal  volume  with  the  body  to  be  determined ;  leaving  us  only  to 
decide  the  loss  of  weight  on  immersion. 

In  order  to  obtain  this  result  easily  by  means  of  a  balance,  the 
instrument  undergoes  a  slight  alteration,  by  which  it  is  converted 
into  a  hydrostatic  balance  (Fig.  76).  We  substitute  for  one  of  the 
usual  scale-pans,  one  that  does  not  hang  down  so  low,  and  to  the 
lower  part  of  which  a  hook  is  attached,  on  which  the  body  to  be 
determined  may  be  suspended.  When  this  is  done,  we  may 
ascertain  the  absolute  weight  g  of  the  body  by  laying  weights  in 
the  other  scale-pan.  If  we  now  immerse  the  body,  we  must 
remove  a  part  a  of  the  weight  g  to  restore  equilibrium;  a  is  con- 


96 


AREOMETER. 
Fig.  76. 


sequently  the  loss  of  weight  sustained  by  the  body  from  immersion, 
and  3-  is,  therefore,  its  specific  gravity. 

Nicholson's  Areometer  (Fig.  77)  may  be  used  to  determine  the 
specific  gravity  of  solid  bodies,  instead  of  the  balance.  To  a 
Fig.  77.  hollow  glass  or  metal  body  v,  a  small  heavy  mass 
/  (a  glass  or  metal  sphere  filled  with  lead)  is  sus- 
pended, and  superiorly  there  is  attached  to  it  a 
fine  stem  supporting  a  plate  c,  on  which  small 
bodies  and  weights  may  be  laid.  The  instrument 
floats  vertically  in  the  water,  because  its  centre  of 
gravity  is  very  low  in  consequence  of  the  weight  /. 
The  instrument  is  so  arranged  that  the  upper  part 
of  the  body  v  projects  above  the  water.  If  now 
we  lay  the  body  wrhose  specific  gravity  we  would 
ascertain  upon  the  plate  c,  the  instrument  will 
descend,  and  by  adding  additional  weight,  we  may 
easily  make  it  sink  to  the  pointy  marked  generally 
by  a  line  on  the  rod.  We  remove  the  mineral  or 
other  substance  we  have  been  using,  and  substitute 
in  its  place  as  many  weights  as  will  again  make  the  instrument 
sink  to/.  If,  in  the  place  of  the  mineral,  we  have  had  to  lay  on 
n  grains,  the  weight  of  the  mineral  is  equal  to  n  grains. 

If,  in  this  manner,  we  have  ascertained  the  absolute  weight  of 
the  mineral,  the  n  grains  must  be  again  removed,  and  the  body 


AREOMETER.  97 

laid  in  a  basket  placed  between  v  and  I.  The  instrument  would 
now  again  sink  to  f  if  the  body  laid  in  the  basket  had  not  lost 
weight  by  being  immersed  in  the  water:  we  must,  therefore,  lay 
on  the  plate  the  weight  m  grains,  that  the  body  may  be  immersed 
to  the  mark.  In  this  manner  we  obtain  the  absolute  weight  of  the 
body  n,  and  the  weight  of  an  equal  volume  of  water  m;  the  spe- 

77 

cific  gravity  we  seek  is,  therefore,  — 

m. 

If,  for  instance,  we  have  to  determine  the  specific  gravity  of  a 
diamond,  we  must  lay  it  on  the  plate  and  add  sufficient  weight  to 
make  the  whole  sink  tojT.  If  we  find  after  removing  the  diamond, 
that  we  must  lay  on  1.2  grains  to  cause  the  areometer  to  sink 
again  to  the  same  point,  the  absolute  weight  of  the  stone  would 
be  1.2  grains.  These  weights  must  be  again  taken  away  and  the 
diamond  laid  in  the  basket ;  then,  in  order  to  make  the  instrument 
sink  toy,  we  must  add  0.34  grains  more;  the  weight  of  a  volume 
of  water  equal  in  volume  to  the  diamond  is,  therefore,  0.34  grains, 

1  2 
and  the  specific  gravity  required  is  -!— =3.53. 

The  specific  gravity  of  liquids  may  also  be  determined  by  Ni- 
cholson's areometer.  As  the  instrument  always  sinks  so  far  that 
its  weight,  added  to  the  weight  upon  the  plate,  is  equal  to  the  mass 
of  liquid  displaced,  we  may,  by  the  aid  of  this  instrument,  ascer- 
tain how  much  a  definite  volume  of  water  weighs.  It  is  neces- 
sary, however,  to  know  the  weight  of  the  instrument  itself.  Sup- 
pose this  weight  to  be  n,  we  must  lay  on  some  additional  weight 
to  make  the  instrument  sink  to  f\  if  we  designate  this  addition 
by  a,  then  is  n  +  a  the  weight  of  water  displaced. 

If  we  immerse  the  instrument  in  another  liquid,  we  must  lay 
on  another  weight  b  in  the  place  of  a,  to  make  the  whole  sink  to 
f-j  b  will  be  greater  than  a  if  the  liquid  be  denser,  and  less  than  a 
if  it  be  lighter  than  water.  The  weight  of  the  liquid  displaced  is 
n  +  b ;  but  its  volume  is  exactly  as  great  as  the  volume  of  the 
mass  of  water,  whose  weight  is  n  +  a,  because  the  areometer  has 
sunk  equally  deep  in  both  cases. 

Suppose  the  instrument  weigh  70  grains,  we  must  add  20 
grains  to  make  it  sink  in  water,  and  1.37,  that  it  may  sink  to 
the  pointy*  in  spirits  of  wine ;  then  the  specific  gravity  of  spirits  of 

70  +  1.37 
wine  is  2Q~  0.793. 


98  AREOMETER. 

The  delicacy  of  the  areometer  is  proportionate  to  the  slightness 
of  stem  in  comparison  with  the  immersed  volume. 

It  is  always  a  somewhat  tedious  process  to  ascertain  the  specific 
gravities  of  liquids  with  this  areometer,  and  we  might  effect  our 
purpose  as  quickly  and  with  much  more  exactness  by  means  of 
the  balance,  in  the  manner  already  indicated.  But  it  often  hap- 
pens for  practical  purposes,  that  we  desire  to  obtain  by  a  short 
process  the  specific  gravity  of  a  fluid  in  as  simple  a  manner  as 
possible,  in  order  to  estimate  its  quality.  In  such  cases,  it  is 
quite  sufficient  to  obtain  the  specific  gravity  within  a  couple  of 
decimal  places,  and  this  purpose  is  most  readily  effected  by  means 
of  the  graduated  areometer,  which  we  will  now  consider. 

The  graduated  Jlreometer. — By  means  of  Nicholson's  areometer 
the  specific  gravity  of  a  liquid  is  obtained  by  a  comparison  of 
the  absolute  weights  of  equal  volumes.  But  the  use  of  the 
graduated  areometer  is  based  upon  the  principle  that,  with 
equal  absolute  weights,  the  specific  gravities  are  inversely  as 
their  volumes. 

Fig.  78  represents  a  graduated  areometer.  It  usually  consists 
of  a  cylindrical  glass  tube,  which  is  enlarged  at  the  bottom  as 
represented  in  the  drawing.  The  lower  ball  is  partially 
filled  with  mercury,  to  enable  the  instrument  to  float 
upright.  If  we  now  suppose  the  instrument  to  be  float- 
ing in  the  water,  the  weight  of  the  water  displaced  is 
equal  to  the  weight  of  the  instrument.  If  we  now  im- 
merse it  in  another  liquid,  it  will  sink  to  a  greater  or 
less  depth,  according  to  whether  the  liquid  is  lighter 
or  heavier  than  water.  Supposing  that  the  areometer 
weigh  ten  grammes,  it  will  displace  ten  cubic  centi- 
metres when  floating  in  water.  If  we  immerse  it  in 
spirits  of  wine,  it  will  sink  so  low  that  the  spirits  of 
wine  displaced  will  also  weigh  ten  grammes.  But  ten 
grammes  of  spirits  of  wine  occupy  more  space  than  ten 
grammes  of  water ;  the  instrument  must,  therefore,  sink 
so  deep  that  the  volume  immersed  in  the  spirits  of  wine 
shall  be  inversely  to  the  volume  immersed  in  water  as 
the  specific  gravity  of  these  liquids. 
We  may  now  well  understand  that,  if  the  tube  be  properly 
divided,  we  may  ascertain  the  specific  gravity  of  a  liquid  by  one 
single  easily-conducted  experiment.  Amongst  all  the  scales  that 


AREOMETER.  99 

have  been  applied  to  the  areometer,  the  one  proposed  by  Gay 
Lussac  is  incontestably  the  simplest  and  most  efficacious ;  we  will 
therefore  consider  it  first. 

We  must  suppose  the  point  a  of  the  tube  of  an  areometer  to 
be  marked  as  being  the  point  to  which  the  instrument  sinks  in 
water,  and,  starting  from  thence,  that  a  series  of  lines  are  so 
arranged  that  the  volume  of  the  portion  of  the  tube  intervening 
between  two  marks  is  y^tn  Part  °f  tne  volume  immersed  in  the 
water.  If,  for  instance,  we  assume  that  the  volume  of  the  sub- 
merged portion  of  the  areometer  is  exactly  ten  cubic  centimetres, 
then  the  volume  of  the  portion  of  the  tube  intervening  between 
the  two  marks  would  be  0.1  of  a  cubic  centimetre. 

The  watermark  a  is  numbered  100,  and  the  divisions  are  num- 
bered upwards.  Areometers  thus  graduated  are  designated  by 
the  special  term  volumeters.  Supposing  that  the  areometer  sank 
in  any  liquid  to  the  mark  80  on  the  volumeter,  we  know  that  80 
parts  of  this  liquid  weigh  as  much  as  100  of  water;  the  specific 
gravity  of  this  liquid  is,  therefore,  to  that  of  water  as  100  to  80, 
and  consequently  =  V/  or  1.25. 

If  the  volumeter  were  to  sink  in  another  liquid  to  the  mark 
116,  we  should  find  by  a  similar  mode  of  deduction  that  the 
specific  gravity  of  this  liquid  was  yff  or  0.862.  In  short,  if  the 
volumeter  sink  to  a  definite  point  j  of  the  scale,  we  find  the  specific 
gravity  s  of  the  liquid,  on  dividing  100  by  the  number  observed 

1 00 

upon  the  graduated  scale;  that  is,  s  = 

The  accuracy  of  such  an  instrument  is  increased  in  proportion 
to  the  distance  of  one  mark  from  the  other,  and  in  proportion  to 
the  thinness  of  the  tube  in  comparison  with  the  volume  of  the 
whole  instrument.  In  order  to  avoid  having  very  long  tubes,  no 
volumeter  is  made  applicable  to  all  fluids,  there  being  different 
ones  that  can  be  used  either  for  lighter  or  heavier  fluids.  In  the 
former,  the  watermark  100  is  near  the  lower;  and  in  the  latter, 
near  the  upper  extremity  of  the  tube. 

Before  the  graduation  is  made,  the  quantity  of  mercury  in  the 
ball  of  the  instrument  must  be  so  regulated  that  it  will  sink  it  in 
the  water  either  to  a  point  lying  near  the  lower  or  upper  end  of 
the  tube.  When  this  is  done,  a  second  point  in  the  scale  must 
be  obtained  in  the  following  manner: — 

Suppose  the  instrument  to  be  intended  for  heavy  liquids,  and, 


100 


AREOMETER. 


therefore,  having  the  watermark  at  the  upper  end  of  the  tube. 
We  provide  ourselves  with  a  liquid  whose  specific  weight  is 
exactly  1.25,  and  which  we  can  easily  obtain  by  a  mixture  of 
water  and  sulphuric  acid,  its  specific  gravity  being  tested  by 
means  of  the  balance.  In  this  liquid  we  now  immerse  the  instru- 
ment, observing  the  mark  to  which  it  sinks.  But  the  specific 
gravity  1.25  corresponds  to  the  mark  80  of  the  volumeter  scale. 
This  last  observed  point  is,  therefore,  to  be  marked  80,  and  the 
intervening  space  to  be  divided  into  twenty  equal  parts ;  a  similar 
graduation  being  carried  on  below  the  point  80. 

If  the  volumeter  be  designed  for  light  liquids,  and  the  mark 
100  be  consequently  at  the  lower  part  of  the  tube,  we  find  a 
second  point  in  the  scale  on  immersing  the  instrument  into  a 
mixture  of  water  and  spirits  of  wine,  the  specific  gravity  of  which 
is  accurately  0.8.  This  specific  gravity  0.8  corresponds  to  the 
mark  125,  and  we  must,  therefore,  divide  the  space  between  this 
mark  and  the  watermark  into  twenty-five  equal  parts.  The  divi- 
sions are  generally  marked  upon  a  strip  of  paper,  and  fastened  to 
the  interior  of  the  tube. 

The  relation  existing  between  the  different  graduated  points  of 
the  volumeter,  and  the  specific  gravity  will  easily  be  understood  by 

looking  at  the  accompanying 
diagram.  The  line  a  b  (Fig. 
79)  represents  a  volumeter 
scale,  ranging  from  the  mark 
50  to  the  mark  130.  At  every 
tenth  point  of  division  a  per- 
pendicular is  drawn,  on  which 
is  marked  the  length  propor- 
tionate to  the  corresponding 
specific  gravity.  Thus,  if  the 
perpendicular  drawn  through 
the  point  100  is  1,  that  through 
50  is  2,  that  through  120  is 
0.83,  and  so  forth;  it  is  of  course  quite  immaterial  what  unit  we 
choose  in  the  graduation  of  these  perpendiculars. 

The  summits  of  these  perpendiculars  are  connected  by  a  curved 
line,  which  represents  the  law  connecting  the  points  of  the  scale 
and  the  corresponding  specific  gravities.  The  curve  ascends  the 
more  rapidly  as  it  approaches  the  lower  points  of  the  volumeter 


2 
1.8 
1.6 
1.4 
1.2 

0.8 

m 
a 

\ 

\ 

\ 

K 

X, 

"*-^ 

x 

l 

8 

G 

4 

2 

08 

50   60  70   80  90  100  110  120  130 


AREOMETER.  101 

scale  lying  near  a.  From  this  it  is  evident  that  the  difference 
between  the  perpendiculars  drawn  through  60  and  70  must  be 
greater  than  that  existing  between  the  equally  distant  perpen- 
diculars drawn  through  120  and  130;  or,  in  general  terms,  that 
an  equal  number  of  degrees  on  the  lower  end  of  the  volumeter 
scale  correspond  with  a  greater  difference  of  specific  gravity  than 
on  the  upper  part.  It  further  follows  that,  if  the  graduated  points 
of  the  scale  are  to  correspond  to  equal  differences  of  the  specific 
gravity,  the  distance  between  two  points  must  be  greater  at  the 
upper  than  at  the  lower  part  of  the  scale. 

Another  excellent  mode  of  dividing  the  areometer  scale,  pro- 
posed also  by  Gay  Lussac,  but  previously  made  use  of  by  Brisson 
and  G.  G.  Schmidt,  gives  the  specific  gravities  directly.  The 
relation  of  this  scale  to  the  volumeter  scale  will  be  easily  under- 
stood. If  we  mark  on  any  of  the  perpendiculars  (Fig.  79)  the 
heights  0.8,  1,  1.2,  1.4,  1.6,  &c.,  and  draw  horizontal  lines 
through  these  heights  to  intersect  the  curve,  and  from  these  points 
of  intersection  perpendiculars  down  to  the  line  representing  the 
volumeter  scale,  or,  as  is  the  case  in  our  diagram,  to  a  line  m  n, 
lying  somewhat  above  that  of  the  volumeter  scale,  we  obtain  the 
degrees  upon  the  scale  coinciding  with  the  specific  gravities  1.8, 
1.6,  1.4,  &c.  But  we  here  see  how  unequal  are  the  divisions  of 
the  scale,  and  how  much  they  increase  in  size  from  the  lower 
towards  the  upper  parts. 

We  have  here  only  given  the  construction  of  this  scale  for  the 
points  from  20  to  20  p.  c.  of  the  specific  gravity.  If  we  wish  to 
construct  a  scale  according  to  this  method,  the  figure  must  be 
drawn  according  to  much  larger  proportions,  and  the  points  from 
at  least  5  to  5  p.  c.  of  the  specific  gravity  must  be  obtained. 
The  intervals  may  then  be  divided  equally  without  any  marked 
error. 

Another  method  of  constructing  these  scales  has  been  proposed 
by  Schmidt.  Although  the  specific  gravity  may  be  obtained 
directly  by  means  of  areometers  of  this  kind,  the  volumeter  has 
great  advantages.  In  the  first  place,  the  completion  of  a  volumeter 
scale  is  infinitely  easier ;  owing  to  the  uniformity  of  the  divisions, 
we  may  graduate  the  scale  with  much  greater  accuracy,  while  the 
calculations  that  have  to  be  made  to  learn  the  specific  gravity 
according  to  the  volumeter  scale,  are  so  extremely  simple  that  they 


102  ALCOHOLOMETER. 

certainly  cannot  furnish  any  grounds  of  objection  to  the  use  of 
that  instrument. 

In  a  practical  point  of  view,  our  aim  is  not  so  much  to  learn 
the  specific  gravity  of  a  liquid  astto  know  the  point  of  concentra- 
tion of  a  saline  solution  and  the  proportion  of  mixture  in  a  liquid. 
These  points  certainly  stand  in  such  close  relation  to  the  specific 
gravity,  that,  if  by  help  of  the  areometer  we  can  ascertain  the 
specific  gravity  of  a  liquid,  we  may  also  draw  a  correct  conclu- 
sion as  to  its  nature.  Special  areometers  have  been  constructed 
for  such  liquids  as  are  most  frequently  used,  giving  the  direct 
proportions  of  mixture.  We  will  only  consider  one  of  the  most 
important  of  these — the  alcoholometer. 

This  instrument  serves  to  determine  the  amount  of  alco- 
Fig.  80.  -j^j  jn  a  mixture  Of  water  and  spirits  of  wine. 

The  specific  gravity  of  alcohol  is  0.793  if  we  take  that 
of  water  as  unity;  a  mixture  of  water  and  absolute  alco- 
hol will,  therefore,  have  a  density  falling  between  1  and 
0.793,  and  approaching  more  nearly  to  either  extremity 
as  the  water  or  the  alcohol  preponderates  in  the  mixture. 
The  density  deviates,  however,  from  the  arithmetical  mean 
reckoned  from  the  proportions  of  the  mixture. 

The  reason  of  this  deviation  is  to  be  sought  in  the  con- 
traction occurring  when  we  mix  water  and  spirits  of 
wine,  and  which  we  will  first  make  evident  by  an  expe- 
riment. 

If  we  take  a  glass  tube,  such,  for  instance,  as  is  used 
in  the  Torricellian  experiment,  fill  one-half  with  water 
and  the  remainder  with  spirits  of  wine,  (for  the  Lecture  Room, 
the  colored  spirit  of  wine  is  preferable,)  we  shall  find  the  liquids 
do  not  mix,  the  spirits  of  wine  floating  on  the  water.  When  the 
open  end  has  been  closed  by  a  cork  stopper,  so  that  no  liquid  can 
escape,  a  mixture  of  the  fluids  will  occur  by  the  sinking  of  the 
water  as  soon  as  we  invert  the  tube.  When  the  liquids  are  per- 
fectly mixed,  we  see  that,  instead  of  the  whole  tube  being  full,  a 
vacuum  has  been  formed,  and  occupying  about  half  an  inch  of 
the  tube. 

The  accompanying  figure  (Fig.  81)  represents  the  laws  for  the 
contraction  of  different  proportions  of  mixture.  The  perpendicu- 
lars drawn  at  the  different  points  of  the  horizontal  bases  of  the 
parallelogram,  and  passing  through  its  upper  side,  give  the  sums 


ALCOHOLOMETER. 


103 


of  the  mixed  volumes,  the  part  lying  within  the  shaded  portion  of 
the  figure  showing  the  volume  of  the  water, 
and  the  remainder  the  volume  of  the  spirits 
of  wine.  Thus,  the  perpendicular  line 
elevated  at  the  point  20  is  divided  by  the 
diagonal  of  the  parallelogram  in  such  a 
ratio  that  T8oths  of  its  whole  length  fall  with- 
in the  shaded,  and  the  remaining  Tyhs  in 
the  unshaded  part  of  the  figure ;  it  corre- 
sponds, therefore,  to  a  case  where  we  have 
a  mixture  of  80  parts  water  with  20  parts 
spirits  of  wine.  But  in  this  case,  the  mix- 
ture forms  a  volume  only  0.982  of  the 
sum  of  the  mixed  volumes,  on  which  account  the  length  of  0.982 
is  marked  upon  this  perpendicular,  counting  from  below  (taking 
the  whole  length  of  the  perpendicular  as  the  unit).  Thus  the 
length  0.965  is  marked  at  the  point  60,  because  40  p.  c.  of  water 
mixed  with  60  p.  c.  of  spirits  of  wine  coincide  with  0.965,  the 
sum  of  the  mixed  volumes.  The  numbers  standing  over  every 
perpendicular  give  for  each  case  the  exact  value  of  the  volume 
according  to  the  mixture,  if  the  sums  of  the  mixed  volumes  be 
1000.  A  curve  is  drawn  over  the  points  marked  in  the  way  in- 
dicated on  the  different  perpendiculars.  The  vertical  distance 
between  each  point  of  this  curve  from  the  upper  horizontal  line 
represents  the  amount  of  the  contraction. 

From  these  considerations  it  follows  that  the  specific  gravity  of 
a  mixture  of  water  and  spirits  of  wine  must 
always  be  greater  than  the  computed  arith- 
metical mean.  In  Fig.  82,  0.793  is  the 
length  of  the  perpendicular  drawn  through 
the  point  100,  if  we  take  the  length  of  the 
perpendicular  from  the  point  o  as  the  unity. 
The  former  represents  the  specific  gravity 
of  absolute  alcohol,  and  the  latter  that  of 
water.  If  we  connect  the  upper  points  of 
these  two  extreme  perpendiculars  by  a 
straight  line,  and  draw  through  the  points 
90,  80,  70,  &c.,  perpendiculars  going  to  10° 
this  straight  line,  the  length  of  these  perpendiculars  would  repre- 
sent the  specific  gravity  of  a  mixture  of  90,  80,  70,  &c.,  parts  of 


Fig.  82. 


OOOO    OOOOOOrH 


80      60      40      20 


104  ALCOHOLOMETER. 

spirits  of  wine  with  10,  20,  30,  &c.,  parts  of  water,  if  no  con- 
traction occurred.  But  a  length  is  marked  upon  every  perpen- 
dicular corresponding  to  the  true  density  of  the  mixture.  The 
curve  connecting  those  points  in  the  different  perpendiculars  re- 
presents the  law  according  to  which  the  density  of  a  mixture  of 
water  and  spirits  of  wine  changes,  if  the  alcoholic  contents  increase 
from  0  to  100  p.  c. 

The  number  standing  over  each  perpendicular  gives  the  accu- 
rate numerical  value  of  the  specific  gravity  of  the  corresponding 
mixture.  If  by  the  numbers  100,  90,  80,  20,  10,  0,  we  designate 
those  points  on  an  areometer-tube  that  correspond  with  the  specific 
gravities  0.793,  0.828,  0.857,  0.976,  0.985,  and  1 ;  and  if,  further, 
we  divide  the  space  intervening  between  every  two  points  into 
ten  equal  parts,  which  may  be  done  without  any  great  inaccuracy, 
we  obtain  a  per-centage  areometer  for  spirits  of  wine ;  that  is  to 
say,  an  instrument  by  which  we  can  directly  read  off  how  many 
parts  by  volume  of  alcohol  are  contained  in  a  mixture  of  water 
and  spirits  of  wine.  Such  alcoholometers  have  been  made  in 
France  according  to  the  calculations  of  Gay  Lussac,  and  in  Ger- 
many according  to  those  of  Tralles,  and  have  been  officially 
adopted,  in  order  that  by  their  aid  the  alcoholic  contents 
100  of  brandy,  spirits  of  wine,  &c.,  subject  to  excise  duties, 
might  be  determined.  Fig.  83  shows  the  main  divi- 
sions of  such  an  alcoholometer  in  their  true  proportions. 
We  see,  as  we  might  suppose,  that  the  divisions  are  of 
unequal  magnitude. 

The  volumeter  may  easily  replace  the  alcoholometer, 
if  we  only  have  at  hand  a  table  in  which  the  quantity 
of  alcohol  corresponding  with  the  different  degrees  of 
the  volumeter  is  given. 

As  may  easily  be  supposed,  the  alcoholometer  is  not 
applicable  to  any  other  fluid  than  the  one  for  which  it  is 
-•  50  designed.  In  a  similar  manner  areometers  have  been 
40  constructed  for  giving  accurately  the  proportions  of  an 
J.  so  acid,  a  saline  solution,  &c.  As,  however,  such  instru- 
10  ments  are  solely  applicable  to  the  single  fluids  for  which 
they  are  constructed,  it  is  better  to  make  use  of  the  vo- 
lumeter, and  to  seek  in  the  tables  constructed  for  the 
purpose,  the  proportions  corresponding  to  the  degrees  observed 
on  the  volumeter. 


TABLE    OF    SPECIFIC    WEIGHTS.  105 

It  now  only  remains  for  us  to  mention  the  older  areometric  gra- 
duations, which,  however,  are  no  longer  of  use  for  scientific  pur- 
poses. 

Beaume  fixed  on  a  second  point,  in  addition  to  the  watermark, 
by  plunging  the  instrument  into  a  solution  consisting  of  one  part 
of  common  salt  and  nine  parts  of  water.  The  space  intervening 
between  these  two  points  he  divided  into  ten  equal  parts,  which 
he  called  degrees,  the  division  being  continued  beyond  the  two 
fixed  points.  The  water  point  is  marked  with  0  for  liquids  heavier 
than  water  when  the  degrees  are  counted  downwards,  while  for 
liquids  lighter  than  water,  the  water  point  is  marked  10,  and  the 
degrees  are  counted  upward.  It  is  easy  to  see  that  by  such  an 
instrument  neither  the  specific  weight  nor  the  proportions  of  a 
fluid  mixture  can  be  ascertained. 

Cartier  made  an  unimportant  change  in  Beaume's  scale  by 
increasing  the  size  of  the  degrees,  fifteen  of  his  degrees  being 
equal  to  sixteen  of  Beaume's  instrument.  However  little  benefit 
may  have  been  derived  from  this  alteration,  it  has  had  the  effect 
of  handing  down  his  name  to  posterity,  since,  in  spite  of  its  little 
value,  Cat  tier'' s  scale  is  very  generally  known. 

In  Germany,  Meiszner  has  done  much  service  to  areometry, 
and  his  treatise,  published  in  1816,  at  Vienna,  "  On  the  Applica- 
tion of  Areometry  to  Chemistry  and  Technology"  is,  perhaps, 
the  most  valuable  work  that  we  have  on  the  subject.  Meiszner's 
areometers  consist  of  simple  cylindrical  glass  tubes  from  six  to 
eight  millimetres  in  diameter,  without  enlargement  at  the  lower 
end,  which  is  filled  with  shot  imbedded  in  fused  sealing  wax;  the 
scale  is  at  the  upper  end. 

The  following  table  gives  a  view  of  the  specific  gravities  of  cer- 
tain bodies,  the  knowledge  of  which  may  frequently  prove  neces- 
sary, or'  at  least  interesting. 

TABLE    OF    THE    SPECIFIC    WEIGHTS    OF    SOME    SOLID    BODIES. 

Platinum— coined  .  .  22.100  Iridium 18.600 

"  rolled  .  .  .  22.069  Tungsten  ....  17.600 

"  fused  ....  20.857  Lead— fused  .  .  .  11.352 

"  drawn  into  wire  19.267  Palladium  ....  11.300 

Gold— coined  .  .  .  19.325  Silver 10.474 

"  fused  .  .  19.258  Bismuth  .  9.822 


106 


TABLE    OF    DENSITY    OF    LIQUIDS. 


Copper—  malleable      .     8.878 
"     fused  ....     7.788 
"     drawn  into  wire      8.780 
Cadmium      ....     8.694 
Molybdenum     .     .     .     8.611 
Brass       8.  395 

Sulphate  of  Lime  (Crys- 
tal) 

2.311 
2.033 
1.917 
1.874 
1.800 
1.770 
1.078 
0.960 
0.972 
0.865 
1.226 
1.170 
1.330 
0.904 
0.659 
0.982 
0.590 
0.890 
0.555 
0.857 
0.500 
0.904 
0.644 
0.945 
0.769 
0.817 
0.439 
1.060 
0.677 
0.598 
0.561 
0.383 
0.240 

ISE 

2.966 

1.848 

Sulphur  (Natural)  .     . 
Ivory  . 

Alabaster      .... 
Anthracite    .... 
Phosphorus  .... 
Amber     

Arsenic    .... 

.     8.308 

Nickel      .... 

.     8.279 

Uranium       .     .     . 
Steel  

.     8.1 
.     7.816 

Wax  (White)    .     .     . 
Sodium    . 

Cobalt      .... 

.     7.812 

Potassium     .... 
Ebony     

Iron  —  wrought  .     . 
"     cast    .     .     . 
Tin     

.     7.788 
.     7.207 
.     7.291 

Oak  (Old)     .     .     .     . 
Box 

Antimony      .     .     . 
Tellurium     .     .     . 
Chromium    .     .     . 
Iodine      .... 

.     6.712 
.     6.115 
.     5.900 
4.948 

Maple  —  Green  .     .     . 
"        Dry      ... 
Beech  —  Green  .     .     . 
"        Dry      ... 
Pine  —  Green     .     .     . 
"      Dry    .... 
Alder  —  Green    .     .     . 
"       Dry  .... 
Ash  —  Green      .     .     . 
"Dry     .... 
Hornbeam  —  Green 
"            Dry     .     . 
Linden  —  Green      .     . 
"      Dry     ... 
Mahogany    .... 
Nutwood       .... 
Cypress  . 

Heavy  Spar  ....     4.426 
Selenium      ....     4.320 
Diamond       ....     3.520 
Flint  Glass—  French    .     3.200 
"           English  .'    3.373 
"           Frauenhofer3.779 
Bottle  Glass       .     .     .     2.600 
Plate  Glass  ....     2.370 
Tourmaline  (Green)     .     3.155 
Marble     2.837 

Emerald  .... 

.     2.775 

Rock  Crystal      .     . 
Porcelain  —  Dresden 
"          Sevres  . 
"          China  . 

DENSITY    OF    SOME 

Distilled  Water       . 
Mercury  . 

.     2.683 
.     2.493 
.     2.145 
.     2.384 

LIQUIDS    AT 
SPECIF 

.       1.000 

,  13.598 

Cedar      

Poplar     

Cork   

32°    F.,  UNLESS    OTHERW 
TED. 

Bromine  

Sulphuric  Acid 

TABLE    OF    DENSITY    OF    LIQUIDS.  107 


DILUTE    SULPHURIC    ACID,  ACCORDING    TO    DELEZEUNE,  AT    59°  F. 

1.486 

1.595 
1.709 
1.805 
1.840 


0.994 
0.998 
1.022 
0.916 
0.999 
0.852 
0.953 
0.929 
0.915 
0.872 
0.793 
0.715 
1.272 


10 
20 

per  cent,  acid  . 
tt 

.     1.066 
.     1.138 

60  per  cent,  acid  . 
70 

30 

« 

.     1.215 

80 

40 

tt 

.     1.297 

90           « 

50 

tt 

.     1.387 

100 

DILUTE    NITRIC    ACID. 

10 
20 
30 

40 

per  cent,  acid  . 

u 
tt 

.     1.054 
.     1.111 
.     1.171 
.     1.234 

Wines—  Claret  .     . 
"       Champagne 
"       Malaga     . 
"       Moselle     . 

50 

tt 

.     1.295 

"       Rhenish    . 

60 

tt 

.     1.348 

Oils  —  Citron      .     . 

70 

« 

.     1.398 

"     Linseed   .     . 

80 
90 

tt 

.     1.438 
.     1.473 

"     Poppy      .     . 
"     Olive       .     . 

100 
Mill 
Sea 

tt 

£     

.     1.500 
.     1.030 
.     1.026 

"     Turpentine  . 
Alcohol,  absolute    . 
Sulphuric  Ether 
Sulphuret  of  Carbon 

Water    .     .     . 

108        ADHESION    BETWEEN    SOLID    AND    LIQUID    BODIES. 


CHAPTER   IV. 

MOLECULAR    ACTIONS    BETWEEN     SOLID    AND    LIQUID     BODIES,    AND 
BETWEEN  THE  SEPARATE  PARTICLES  OF  LIQUIDS. 

Adhesion  between  solid  and  liquid  bodies. — The  phenomena  of 
adhesion  occurring  between  solid  and  liquid  bodies  are  similar  to 
those  between  solid  bodies ;  that  is  to  say,  liquids  adhere  more  or 
less  strongly  to  the  surfaces  of  solid  bodies.  If,  for  instance,  we 
sprinkle  a  few  drops  of  water  on  a  vertical  glass  plate,  they  will 
partly  remain  hanging  to  it,  instead  of  dropping  down,  as  would 
be  the  case  if  the  gravity  of  the  drops  were  not  counteracted  by 
another  force,  namely,  the  attraction  which  exists  between  the 
particles  of  the  liquids  and  the  surface  of  the  glass. 

This  adhesion  is  also  the  cause  of  liquids  so  easily  running  down 
the  outer  walls  of  the  vessels  when  we  would  pour  them  out ;  and 
to  avoid  this,  we  either  rub  the  outer  rim  of  the  vessels  with  fat, 
or  let  the  liquid  pass  along  a  moistened  glass  rod. 

Capillary  Tubes. — It  has  been  already  mentioned  that  the  upper 
surface  of  a  liquid  contained  in  any  vessel  is  horizontal.  This, 
however,  is  only  true  where  the  molecular  action  exercises  no 
disturbing  influence  upon  the  walls  of  the  vessel.  In  the  vicinity 
of  the  walls,  deviations  from  the  normal  surface  always  occur. 

If  one  end  of  a  glass  tube  be  plunged  into  a  liquid,  the  level  of 

the  liquid  in  the  tube  will  never  be  at  the  same  height  with  the 

upper  surface  of  the  liquid  outside.    For  instance,  when  plunged 

into  water,  the  column  of  the  liquid  rises  in  the  tube  (Fig.  84) ; 

but  if  we  plunge  the  tube  into  mercury,  the 

Fig.  84.         Fig.  85.  r  *. 

top  of  the  column  of  mercury  in  the  tube  will  be 
lower  (Fig.  85).  These  phenomena  of  eleva- 
tion and  depression  are  known  as  capillary 
phenomena,  and  the  force  producing  them  as 
capillary  attraction,  or  simply  capillarity. 
This  force  not  only  acts  in  the  elevation  or 


CAPILLARY    TUBES.  109 

depression  of  liquids  in  tubes,  but  is  at  work  wherever  liquids  are 
in  connection  with  solid  bodies,  or  among  themselves,  or  where 
solid  bodies  are  in  juxtaposition,  or  in  general  where  the  smallest 
particles  of  ponderable  matter  are  in  contact. 

It  is  easy  to  persuade  one's  self  by  experiment,  that  the  difference 
of  height  between  the  surface  of  liquids  in  tubes,  and  that  of  the 
external  fluid  increases  in  proportion  to  the  narrowness  of  the 
bore  of  the  tube.  If  we  plunge  into  water  two  tubes,  of  which 
one  has  twice  as  large  a  diameter  as  the  other,  the  water  will  rise 
twice  as  high  in  the  narrower  tube ;  if  we  plunge  them  into  mer- 
cury, the  liquid  will  be  depressed  twice  as  low  in  the  narrower 
tube. 

The  difference  of  the  level  of  liquids  within  and  without  the 
tubes  is  inversely  as  the  diameter  of  the  tubes.  The  height  of 
the  raised  columns  depends  in  the  above-given  manner  upon  the 
diameters  of  the  tubes ;  but,  if  the  walls  of  the  tubes  have  been 
wetted,  their  thickness  and  substance  are  of  no  importance ;  on 
the  other  hand,  the  height  depends  especially  upon  the  nature  of 
the  liquid.  The  following  is  the  elevation  in  a  tube  of  .05  inches 
in  diameter  for  three  different  liquids: — 

Water  (sp.  gr.  1000)        .         .         .  0.92  inch 
Alcohol  (sp.  gr.  0,8195)   .         .         .  0.36     " 
Oil  of  turpentine  (0,8695)          .         .0.39     " 

We  must  not  omit  to  mention  that  when  a  liquid  rises  in  a  nar- 
row tube,  the  surface  of  the  liquid  column  is  always  concave 
(Fig.  86),  forming  a  hollow  hemisphere  having  the  diameter  of 
the  tube.     If,  on  the  contrary,  there  be  a  depression,  the  top  of 
the  liquid  will  assume  a  convex  form 
(Fig.  87).     These  forms  are  essentially 
dependent  upon  the  elevation  or  depres- 
sion, for  if  we  pass  any  fatty  substance 
over  the  minor  walls  of  the  tube,  and 
then  place  it  into  water,  we  obtain  a 
convex  meniscus,  exactly  as  if  we  had  immersed  an  ordinary 
glass  tube  in  mercury.     It  follows,  therefore,  that  the  differences 
of  the  level  depend  upon  the  form  of  the  meniscus,  and  conse- 
quently, that  all  accidental  causes  which  hinder  the  meniscus  from 
assuming  its  regular  form,  also  modify  the  height  of  the  columns. 
If,  for  instance,  a  tube  be  not  perfectly  smooth  and  clean  inter- 
10 


110    CONNECTION   BETWEEN    THE   PARTICLES    OF    A    LIQUID. 

nally,  indentations  will  appear  at  the  border  of  the  meniscus,  and 
we  then  obtain,  on  frequently  repeating  the  experiment,  very 
various  results. 

The  power  of  blotting-paper  in  taking  up  liquids,  the  action  of 
the  wicks  of  candles  and  lamps,  the  efflorescence  of  saturated 
solutions,  &c.,  all  depend  upon  the  action  of  capillary  tubes.  The 
vessels  of  plants  conveying  the  sap  upwards  from  the  roots  are 
remarkably  minute, *and  act  on  this  principle. 

Connection  between  the  particles  of  a  Liquid. — Although  liquids 
have  no  independent  form,  and  although  their  separate  particles 
admit  of  being  most  easily  displaced,  the  connection  existing 
between  them  does  not  cease,  as  we  see  exemplified  in  the  case 
of  the  formation  of  drops.  If  we  pour  water  upon  a  surface 
strewed  with  lycopodium  seed,  or  mercury  into  a  porcelain  ves- 
sel, drops  almost  spherical  will  be  formed.  If  no  connection 
existed  between  the  separate  particles  of  the  water  and  the  mer- 
cury, they  would  fall  asunder  like  dust ;  in  slowly  pouring  liquids 
from  any  vessel,  they  will  not  fall  in  separate  drops;  such  a  drop 
only  falling  if  its  weight  be  sufficiently  great  to  effect  at  once  a 
separation  from  the  remaining  mass  of  the  liquid. 

The  cohesion  existing  between  the  separate  particles  of  a  liquid 
can  be  directly  measured.  If  a  solid  disc  be  placed  upon  the 
surface  of  a  liquid,  it  can  no  longer  be  lifted  up  in  a  horizontal 
position  with  the  same  force  as  when  hanging  freely  in  the  air ;  a 
greater  or  smaller  additional  force  being  necessary  to  draw  it  up. 

We  make  use  of  the  balance  in  order  to  measure  this  force. 
On  the  one  side  we  hang  a  horizontal  disc,  and  on  the  other  we 
lay  a  balancing  weight  to  establish  equilibrium.  If  the  whole  be 
equipoised,  we  approximate  the  surface  of  a  liquid  to  the  under 
part  of  the  disc  until  they  meet,  and  then,  without  shaking  the 
balance,  we  add  weights  to  the  opposite  side,  remarking  the  quan- 
tity necessary  to  separate  the  liquid  from  the  disc. 

In  order  to  remove  a  glass  disc  of  118mm  (4.6  in.)  diameter, 
different  weights  are  required  for  different  liquids.  As  for  in- 
stance : — 

Water  (sp.  gr.  1.000)    .         .         .  91 1.1 9  grains 
Alcohol         .         .         .         .         .  478.76      " 
Oil  of  turpentine  ....  525.05      " 

A  disc  of  equal  diameter,  and  constructed  either  of  copper  or  any 


CONNECTION    BETWEEN    THE    PARTICLES    OF    A    LIQUID.     HI 

other  substance,  wetted  by  a  liquid,  yields  precisely  the  same 
results.  Adhesion  is,  therefore,  like  capillarity,  independent  of 
the  nature  of  the  solid  bodies,  and  depends  only  upon  the  nature 
of  the  liquids.  It  is  easy  to  see  the  reason  of  this,  for  on  drawing 
it  up  there  always  remains  a  layer  of  the  liquid  on  the  disc ;  the 
liquid,  therefore,  has  not  been  separated  from  the  disc  by  the  pre- 
ponderance of  weight  on  the  other  side,  but  the  molecules  of  the 
liquid  have  been  severed  from  each  other,  and  the  cohesion  of  the 
liquid  has  been  overcome.  The  experiments  adduced,  yield,  there- 
fore, a  measure  for  the  cohesion  of  liquids,  and  for  the  attraction 
existing  between  their  particles,  and  we  thus  see  how  considera- 
ble is  this  attraction,  and  that  it  changes  with  the  nature  of  the 
liquids. 

If  the  upper  surface  of  the  disc  be  not  moistened  with  the 
liquid,  as,  for  instance,  when  we  place  a  glass  disc  on  mercury, 
the  extra  weight  effecting  the  separation  no  longer  expresses  the 
cohesion  of  the  liquid. 

It  is  necessary  to  use  a  force  of  about  200  grammes  (3083  grs.) 
to  raise  a  glass  disc  of  the  above  dimensions.  It  follows,  there- 
fore, that,  even  when  a  solid  body  is  not  moistened  by  a  liquid,  a 
greater  or  smaller  attraction  will  still  exist  between  the  molecules 
of  the  liquid  and  those  of  the  solid  body,  only  in  this  case  the 
cohesion  of  the  liquid  is  greater  than  the  adhesion  between  the 
liquid  and  the  solid  body. 

The  phenomena  here  treated  of  may  be  considered  in  a  theore- 
tical point  of  view,  in  the  following  manner: — Mercury  forms 
spherical  drops  upon  paper,  and  water  upon  an  unctuous  or 
sprinkled  surface. 

This  phenomenon  is  usually  explained  by  the  universal  attrac- 
tion of  all  molecules  to  one  another,  on  the  same  principle  that 
we  explain  the  spherical  formation  of  the  heavenly  bodies.  But 
this  explanation  is  not  admissible,  since  molecular  attraction  acts 
very  differently  from  universal  gravity ;  and  since,  from  its  acting 
only  at  imperceptible  distances  upon  contiguous  molecules,  it 
cannot  be  so  condensed  as  to  form  a  central  point  of  attraction 
similar  to  the  central  point  of  gravitation  of  the  planets.  The 
following  seems  to  be  a  more  correct  mode  of  elucidating  the 
subject: — 

The  molecules  of  a  liquid  must  remain  at  such  a  distance  that 
attraction  and  repulsion  shall  neutralize  each  other.  This  is  only 


112    CONNECTION   BETWEEN   THE    PARTICLES    OF    A    LIQUID. 

possible  when  the  molecules  are  so  placed  in  regular  layers  that 
each  molecule  is  surrounded  by  twelve  others,  somewhat  in  the 
manner  that  cannon  balls  of  equal  size  are  wont  to  be  ranged. 
This  arrangement  remains  also  undisturbed  where  the  liquid  ter- 
minates in  a  level  surface.  Every  molecule  is  subject  to  perfectly 
equal  actions  from  all  sides,  and  all  the  molecules  are  perfectly 
equidistant  one  from  the  other.  Such  an  arrangement  may  be 
termed  the  normal  arrangement  of  the  molecules.  If  a  part  of 
the  limiting  surface  be  curved,  the  reciprocal  apposition  of  the 
molecules  can  no  longer  remain  the  same ;  and  such  a  disposition 
may  be  termed  abnormal. 

As  soon  as  the  normal  position  of  the  molecules  is  disturbed  by 
any  external  force,  the  hitherto  perfect  equilibrium  of  the  whole 
will  be  disturbed,  a  tension  will  arise,  striving  to  restore  the  dis- 
turbed parallelism  of  the  layers,  and  bring  back  the  particles  of 
the  liquid  to  their  normal  position  as  soon  as  the  disturbing  cause 
ceases  to  act.  If  we  plunge  a  rod  moistened  by  a  liquid  into 
the  same,  we  may,  by  slowly  drawing  it  out,  form  an  elevation 
which  will  immediately  be  restored  to  a  plane  surface  on  entirely 
removing  the  rod. 

This  certainly  can  only  be  the  consequence  of  gravity;  but 
the  same  thing  occurs  in  the  reversed  position  of  the  plane.  If 
we  fill  with  water  a  tube  not  exceeding  three  lines  in  diameter, 
and  having  one  end  open,  we  may  revolve  it  without  the  water 
escaping.  It  forms  a  hanging  plane,  from  which,  as  in  the 
former  instance,  then  arise  elevations,  which,  after  separation,  in 
opposition  to  the  action  of  gravity,  return  to  the  plane  surface. 

A  liquid  strives,  therefore,  to  terminate  in  a  plane  surface ;  but 
a  mass  free  on  all  sides  cannot  be  surrounded  by  one  single  plane. 
If  it  were  bounded  by  plane  surfaces,  the  edges  would  be  soon 
flattened  by  the  tension  of  the  molecules;  but,  if  the  mass  were 
bounded  by  a  curved  surface,  whose  curves  were  not  equal  on  all 
sides,  a  stronger  tension  would  naturally  also  occur  at  the  more 
strongly  curved  parts  of  the  surfaces,  tending  to  the  perfect 
sphericity  of  the  whole.  The  roundness  of  the  air-bubble  de- 
pends upon  the  same  principle.  The  superficial  molecules  of 
a  perfectly  free  liquid  compose,  therefore,  a  net-work,  forcibly 
compressing  the  minor  part.  If  we  make  a  soap-bubble,  it  will 
retain  its  size  as  long  as  we  keep  the  opening  of  the  tube  closed, 
but,  as  soon  as  this  ceases  to  be  done,  the  bubble  will  diminish 


CONNECTION   BETWEEN    THE   PARTICLES    OF    A   LIQUID.     H3 

more  and  more.  If  the  air  in  the  bubble  were  not  compressed 
by  the  enclosing  liquid,  and  if  it  were  not  denser  than  the  sur- 
rounding atmosphere,  it  would  remain  in  the  bubble,  and  not  be 
forced  into  the  tube  against  the  atmospheric  pressure  of  the  air. 

If  mercury  is  put  into  a  glass,  it  will  stand  off  from  the  sides 
of  the  vessel,  although,  perhaps,  not  perceptibly;  if,  however,  we 
add  water  or  olive  oil,  either  will  fill  the  interval.  In  badly  pre- 
pared barometers,  air  will  also  force  itself  through  this  interval 
into  the  Torricellian  vacuum.  The  mercury  forms  a  large  drop 
lying  free  in  the  glass,  and  its  form  depends  upon  the  walls  of 
the  vessel.  It  terminates  superiorly  in  a  horizontal  surface, 
which,  however,  cannot  reach  to  the  sides  of  the  vessel,  owing  to 
the  sharp  edge  of  the  drop  having  been  rounded  off,  as  we  have 
before,  said. 

If  a  drop  of  mercury  be  poured  into  a  perfectly  cylindrical  glass 
tube  placed  horizontally,  the  drop  will  form  a  cylinder  rounded  at 
either  end.  No  motion  can,  however,  arise,  as  the  convexity  is 
equal  at  both  ends. 

But,  if  the  tube  be  conical  (Fig.  88),  the  mercury  will  be  more 
curved  at  the  narrower  end ;  the  ten- 
sion of  the  abnormally  placed  mole- 
cules is,  therefore,  greater  here  than 
on  the  other  side,  and  the  consequence 
of  this  preponderating  tension  is,  that  the  mercury  moves  to  the 
wider  end. 

If  we  entirely  fill  a  narrow  tube  with  mercury,  and  place  it 
horizontally,  letting  the  one  end  communicate  with  a  drop  of 
mercury  at  the  extremity  of  the  tube,  the  latter  will  increase  until 
the  mercury  at  length  entirely  leaves  the  tube,  and  is  collected  in 
one  large  drop.  The  reason  of  this  is  easily  understood.  By  the 
strong  'curvature  of  the  convexity  at  the  end  of  the  cylinder  of 
mercury,  there  arises  on  this  side  a  far  stronger  pressure  on  the 
mass  than  on  the  side  of  the  drop. 

If  a  glass  tube  be  plunged  vertically  into  mercury,  the  liquid 
will  be  deeper  within  than  without  the  tube,  as  the  strong  con- 
vexity of  the  cylinder  of  mercury  acts  depressingly  in  the  tube. 
It  is  also  clear  that  the  narrower  the  tube,  the  greater  will  be  the 
depression. 

If  a  liquid  adhere  to  the  walls  of  the  vessel  and  wets  them, 
it  can  no  longer,  as  in  the  former  instance,  be  regarded  as  a 

10* 


114    CONNECTION   BETWEEN   THE   PARTICLES    OF    A    LIQUID. 

large  drop;  the  upper  surface  cannot,  therefore,  assume  a  con- 
vex form.  The  molecules  of  the  walls  of  the  vessel  in  contact 
with  the  liquid  act  upon  the  latter  as  the  molecules  of  the  liquid 
upon  one  another.  The  solid  walls  of  the  vessel  are,  therefore, 
only  to  be  considered  as  a  rigid  continuation  of  the  liquid.  The 
air  above  the  liquid  in  the  vessel  must,  therefore,  be  regarded  as 
a  bubble,  bounded  inferiorly  by  the  liquid,  and  on  all  sides  by  the 
walls  of  the  vessel.  If  the  surface  of  the  liquid  were  perfectly 
even,  the  bubble  would  have  a  sharp  edge  where  the  fluid  and 
the  walls  of  the  vessel  came  in  contact,  which  would  immediately 
be  rounded  off  by  the  mutual  attraction  of  the  molecules  of  the 
wall  and  the  fluid ;  as,  however,  the  molecules  of  the  vessel  are 
solid,  the  surface  of  the  liquid  must  necessarily  assume  a  concave 
form,  while  the  molecules  of  the  liquid  ascend  the  sides  of  the 
vessel.  In  the  bubble,  however,  the  tension  of  the  abnormally 
placed  molecules  of  water  exercises  a  pressure  upon  the  enclosed 
air ;  and  then  the  concave  surface  of  the  liquid  also  exercises  an 
upward  pressure  against  the  air  of  the  bubble.  A  drop  of  water 
in  a  horizontal  cylindrical  glass  tube  will  form  a  cylinder  concave 
at  both  ends,  and  stationary,  owing  to  the  concavity  being  equal 
at  both  ends.  If  the  tube  be  conical,  the  one  concavity  must 
necessarily  be  more  strongly  curved  than  the  other,  and,  by 
the  preponderating  tension  of  the  stronger  curved  extremity,  the 

water  will    be    drawn  towards   the 
narrower  part  of  the  tube  (Fig.  89). 
In  the  same  manner  we  may  easily 
explain,    by  the   action   of  concave 
surfaces,  the  rising  of  water  in  a  tube  plunged  vertically  into  that 
liquid. 

If  a  hollow  glass  sphere  swim  on  water,  the  liquid  will  begin 
at  a  distance  of  more  than  six  lines  to  rise  against  the  ball.  If 
now  we  put  a  second  glass  sphere  into  the  water,  at  about  one 
inch  from  the  former,  the  balls  will  begin  to  approach  each  other, 
at  first  slowly,  then  more  and  more  rapidly,  until  they  finally 
strike  one  another  (Figs.  90  and  91).  If  both  balls  had  been 
fixed,  the  water  between  the  balls  would  have  risen,  in  conse- 

Fig.  90.  Fig.  91. 


ELASTICITY    OF    LIQUIDS.  115 

quence  of  its  striving  to  come  to  a  level ;  but,  as  they  are  move- 
able,  the  adhering  water-surfaces  sinking  from  the  action  of 
gravity  must  draw  together  the  balls  between  which  they  were 
interposed. 

Elasticity  of  Liquids. — Liquid  bodies  are  also  in  some  respects 
elastic,  for  they  allow  themselves,  by  means  of  a  very  strong 
pressure,  to  be  reduced  to  a  volume  somewhat  smaller  than  their 
original  mass,  and  resume  their  former  volume  on  the  removal  of 
the  pressure.  Oersted  first,  and  subsequently  Colladon  and  Sturm 
have  made  experiments  upon  the  compressibility  of  liquids,  but 
we  should  be  drawn  into  too  wide  a  digression  were  we  to  enter 
fully  into  a  description  of  what  they  have  done.  The  pressure 
of  one  atmosphere  (an  expression  that  we  will  explain  in  the 
proper  place)  compresses  mercury  to  about  three,  and  water  to 
about  forty-eight  millionth  parts  of  their  volume. 


116  AIR. 


CHAPTER    V. 

OF  THE  EQUILIBRIUM  OF  GASES,  AND  OF  ATMOSPHERIC  PRESSURE. 

AIR  is  a  body  that  does  not  act  immediately  upon  the  senses  as 
solid  and  liquid  bodies,  but  manifests  itself  by  so  many  pheno- 
mena upon  the  land,  and  over  the  waters  of  the  earth,  that  it  will 
be  unnecessary  to  seek  for  other  proofs  of  its  existence.  There 
are  thunderstorms  in  every  climate,  and  storms  on  every  sea ;  the 
air,  therefore,  everywhere  surrounds  the  whole  globe  of  the  earth, 
forming  at  all  points  a  layer  of  great  thickness  ;  for  clouds  driven 
by  the  winds  pass  alike  over  plains  and  hills.  Above  the  clouds, 
we  see  the  glorious  color  of  the  sky,  evincing  the  height  of  the  air, 
as  the  color  of  the  ocean  does  the  depth  of  its  waters.  If  there 
were  no  air,  the  sky  would  be  without  color  and  brightness,  ap- 
pearing but  as  a  perfectly  black  vault,  in  which  the  stars  would 
appear  with  the  same  splendor  by  day  as  by  night.  This  vast 
mass  of  air  spread  over  the  earth,  and  stretching  high  over  the 
summits  of  the  loftiest  mountains,  bears  the  name  of  the  atmo- 
sphere. The  highest  peak  of  the  Himalaya  scarcely  stretches  five 
miles  above  the  level  of  the  sea,  while  the  air  rises  to  a  height  at 
least  six  or  seven  times  loftier. 

The  chemical  discoveries  of  the  past  century  have  taught  us  to 
know  many  bodies  possessing  the  same  physical  properties  as  the 
air,  although  very  different  in  their  nature.  They  were  termed 
airs,  and  were  spoken  of  as  mephitic,  combustible,  and  fixed  airs. 
In  the  present  day,  they  are  called  gases,  gaseous  bodies,  or  elastic 
fluids. 

Gases  are,  like  liquid  bodies,  subject  to  two  different  forces, 
gravity,  and  molecular  forces. 

At  a  very  remote  period,  even  before  the  time  of  Aristotle,  it 
was  conjectured  that  air  had  weight.  This  truth  was,  however, 
first  proved  by  Galileo,  in  1640,  and  confirmed  somewhat  later  by 
the  beautiful  experiments  of  Torricelli.  The  heaviness  of  the  air 


AIR.  117 

may  be  directly  proved  by  the  following  experiment:  —  Take 
a  balloon  provided  with  a  cock,  and  from  which  the  air  has  been 
removed  by  means  of  an  air-pump ;  hang  it  on  one  arm  of  a 
balance,  and  lay  sufficient  weight  on  the  opposite  side  to  establish 
equilibrium.  If  now  we  turn  the  cock,  the  balloon  will  again  be 
filled  with  air,  the  equilibrium  disturbed,  and  the  balance  inclined 
to  the  side  of  the  balloon.  We  must  now  again  lay  on  sufficient 
weight  to  equipoise  the  whole,  and  this  will  be  precisely  as  much 
as  the  air  in  the  balloon  weighs.  For  a  balloon  of  one  litre,  (61.028 
cubic  inches,)  the  difference  of  weight  amounts  to  more  than  one 
gramme,  (15.444  grs.,)  from  whence  it  follows,  at  a  rough  esti- 
mation, that,  under  ordinary  circumstances,  one  litre  of  air  weighs 
more  than  one  gramme;  that  is,  that  water  is  not  quite  1,000 
times  so  heavy  as  common  air.  [The  weight  of  100  cubic  inches 
of  common  air  at  60°  F.,  has  been  variously  estimated.  Thus 
Kirwan  computes  it  at  30.92  grains,  Davy  at  31.10,  Shuckburgh 
30.5,  and  Brande  at  30.199.] 

Instead  of  a  balloon  with  a  cock,  we  may  use  the  following 
cheap  arrangement,  which  has,  further,  the  advantage  of  weighing 
much  less  under  an  equal  volume  than  the  former.  We  must  take 
a  balloon  of  not  very  thick  glass,  and  not  a  very  narrow  neck 
(Fig.  92).  The  neck  must  be  carefully  closed  with  a  tightly- 
fitting  cork,  perforated  through  the  middle  with  an  opening  about 
two  millimetres  in  diameter.  The  cork  must  now  be  tied  down 
with  oiled  silk,  as  seen  in  Fig.  92,  and  on  a  larger  scale  in  Fig.  93. 
In  this  manner,  the  inner  part  92  Fjo.  93 

of  the  balloon  is  completely 
secured  from  the  access  of  ex- 
ternal air.  Near  the  part  co- 
vering the  opening  of  the  cork, 
we  make  two  cuts  into  the 
oiled  silk,  as  seen  in  Fig.  93, 
and  then  the  balloon  is  to  a  cer- 
tain extent  closed  with  a  valve 
through  which  air  may  escape  from  the  balloon,  but  cannot  enter 
into  it.  In  making  this  experiment  we  first  weigh  the  balloon 
while  full  of  air;  we  then  bring  if  under  the  receiver  of  the  air- 
pump,  when,  on  exhausting  it,  the  air  in  the  balloon  will  also  be 
removed;  when  thus  emptied  it  must  be  re-weighed,  when  we  shall 
find  that  it  has  become  lighter. 


118  AIR. 

Molecular  forces  act  very  differently  in  gases  from  what  they 
do  in  solid  and  liquid  bodies.  We  have  seen  that  these  forces 
hold  firmly  together  the  molecules  of  solid  bodies,  so  that  they 
cannot  change  their  respective  positions.  They  also  hold  together 
the  molecules  of  liquid  bodies,  but  only  in  such  a  manner  as  to 
afford  them  more  freedom  in  displacing  each  other  in  all  directions. 
In  gases,  however,  molecular  forces  act  repulsively,  the  molecules 
of  gaseous  bodies  having  a  tendency  to  move  reciprocally  away 
from  each  other,  and  that  to  so  great  an  extent  that  nothing  but 
external  impediments  can  hinder  their  further  expansion.  The 
air  contained  in  a  vessel  presses,  therefore,  continually  against  its 
sides. 

This  tendency  in  air  to  expand  will  be  easily  shown  by  the 
following  experiment : — We  lay  under  the  receiver  of  the  air- 
pump  an  animal  bladder,  containing  but  little  air,  and,  therefore, 
wrinkled,  having  its  opening  tightly  secured.  After  a  few  strokes 
of  the  piston,  the  bladder  becomes  inflated,  and  at  last  is  tensely 
stretched,  as  if  air  had  been  violently  injected.  If  we  suffer  the 
air  to  return  to  the  receiver,  the  bladder  will  again  shrivel  up. 
The  air  enclosed  in  the  bladder  has,  therefore,  really  a  tendency 
to  expand,  but  meets  with  opposition  from  the  surrounding  air. 
Instead  of  a  bladder  we  might  have  placed  a  thin,  firmly-corked 
glass  under  the  receiver,  when  the  stopper  would  either  have  been 
forced  out,  or  the  glass  would  have  been  burst,  provided  the  cork 
were  not  too  firmly  placed,  or  the  glass  too  strong.  This  pres- 
sure exercised  by  the  air  upon  the  sides  of  the  enclosing  vessel 
is  what  we  term  its  elasticity,  power  of  tension,  or  force  of  ex- 
pansion. 

A  feather  only  manifests  elasticity  if  we  compress  it ;  it  loses 
its  tension  as  soon  as  it  returns  to  its  original  condition.  But 
air  has  always  an  expansive  force ;  it  cannot  be  said  to  have  any 
original  volume,  for  it  always  strives  to  occupy  a  larger  space.  If 
we  were  to  admit  one  litre  of  common  air  into  a  vacuum  of  several 
cubic  metres,  it  would  distribute  itself  equally  throughout  the 
whole  space,  and  would  always  manifest  a  tendency  to  expand, 
exercising,  consequently,  a  pressure  upon  the  enclosing  walls. 

The  construction  of  the  air-pump,  an  instrument  to  which  we 
have  already  repeatedly  alluded,  and  which  we  purpose  now 
describing  more  fully,  depends  upon  the  tendency  manifested  by 
the  air  of  occupying  as  large  a  space  as  possible.  If  the  air  had 


PRESSURE    OF    THE    AIR.  119 

no  power  of  tension,  no  elasticity,  in  the  sense  we  have  ascribed 
to  the  words,  it  could  not  distribute  itself  out  of  the  receiver  of 
the  air-pump;  without  its  tendency  to  expand,  the  air  could  not 
escape  from  the  balloon,  even  if  we  removed  the  weight  of  air 
pressing  from  without  upon  the  valve. 

It  follows,  from  the  expansive  force  of  gases,  that  they  cannot 
be  bounded  by  a  free  even  surface,  as  is  the  case  with  fluids. 
Two  forces,  gravity  and  the  force  of  expansion,  act  upon  the  air 
of  our  atmosphere  and  counterpoise  each  other.  By  gravity  the 
particles  of  the  air  are  attracted  to  the  earth:  this  force,  therefore, 
exercises  a  tendency  to  condense  the  air  upon  the  earth's  surface, 
which  is  counteracted  by  the  force  of  expansion.  The  atmosphere 
is,  therefore,  probably  limited,  as  the  expansive  force  diminishes 
so  much  at  a  certain  degree  of  rarefaction,  that  the  gravity  of  the 
particles  of  air  is  alone  sufficient  to  hinder  a  further  removal  from 
the  earth. 

Pressure  of  the  Mr. — If  the  common  conditions  of  equilibrium 
be  satisfied,  we  may  prove  by  direct  experiment  that  all  the  under 
layers  of  air  are  pressed  upon  by  the  upper,  and  that  the  amount 
of  this  pressure  varies  as  we  ascend  more  and  more  above  the 
level  of  the  sea. 

Let  us  place  a  glass  cylinder,  with  some-  Fig.  94. 

what  thick  sides,  upon  the  plate  of  the  air- 
pump,  and  cover  the  vessel  with  a  bladder 
tightly  stretched,  and  firmly  tied  over  the  top. 
The  bladder  suffers  an  equal  pressure  on  both 
sides,  and  forms,  therefore,  a  level  surface.  If 
now,  by  any  means,  we  force  additional  air 
into  the  cylinder,  the  bladder  will  be  arched  outwards ;  but  if,  on 
the  contrary,  we  remove  any  of  the  air  from  the  cylinder,  the  ex- 
ternal pressure  of  air  will  preponderate,  and  force  the  bladder  in- 
wards. The  latter  may  easily  be  shown  by  means  of  the  air- 
pump.  After  the  first  few  strokes  of  the  piston,  the  bladder  will 
already  be  curved  downwards,  and  the  more  we  exhaust  the  air 
the  more  this  curvature  increases.  If  we  strike  the  bladder  with 
any  sharp  body  when  it  is  thus  stretched,  it  will  be  torn  in  a  thou- 
sand pieces,  with  a  noise  like  the  report  of  a  pistol.  This  sound 
is  produced  by  the  air  forcing  itself  in ;  and  we  may  thus  form 
some  idea  of  the  amount  of  the  pressure  of  air  resting  upon  the 
bladder. 


120  MEASUREMENT    OF   ATMOSPHERIC    PRESSURE. 

If  we  had  so  far  altered  the  experiment  as  to  have  placed  the 
bladder  in  an  oblique  position,  or  made  the  pressure  of  air  act 
from  below,  we  should  have  obtained  the  same  result,  as  the  air 
presses  in  all  directions  in  an  equal  manner. 

This  experiment  appears  very  striking,  when  we  think  that  the 
air  in  a  room  is  able  to  exercise  so  enormous  a  pressure.  This 
effect  cannot  arise  from  the  weight  of  a  column  of  air  resting 
upon  the  bladder,  and  stretching  from  thence  to  the  ceiling  of  the 
'  room,  for  even  a  column  of  water  of  this  height  could  not  produce 
such  a  result.  If  the  experiment  were  made  in  the  open  air,  the 
bladder  would  evidently  have  to  sustain  the  pressure  of  a  column 
of  air  whose  height  is  equal  to  the  height  of  the  whole  atmosphere. 
The  same  pressure  acts  in  a  room,  for  the  air  within  the  room  is 
acted  upon  by  the  whole  pressure  of  the  atmosphere. 

Measurement  of  Atmospheric  Pressure. — As  the  air  surrounds 
the  whole  earth,  it  presses  upon  everything  as  upon  the  bladder, 
upon  the  land  as  upon  the  ocean.  If  we  plunge  one  end  of  a 
tube  into  a  vessel  filled  with  water,  the  fluid  will  rise  as  high 
within  the  tube  as  without,  for  the  pressure  of  the  air  in  the  tube 
acts  precisely  the  same  upon  the  level  of  the  fluid  as  without  the 
tube.  But  if  we  abstract  a  portion  of  the  air  from  the  tube,  the 
fluid  will  continue  to  rise  as  long  as  we  remove  the  air.  By 
this  exhaustion  the  air  within  the  tube  is  diminished,  while  the 
external  pressure  of  the  air  remains  the  same.  The  preponde- 
rance of  the  external  pressure  of  air  raises  the  fluid  within  the 
tube,  until  the  weight  of  this  raised  column  of  water  equipoises 
the  preponderance.  If  we  entirely  exhaust  the  air  in  the  interior 
of  the  tube,  the  water  must  rise  (provided  the  tube  be  high 
enough),  until  the  weight  of  the  raised  column  of  water  is  equal 
to  the  weight  of  a  column  of  air  of  the  same  base  reaching  to  the 
limits  of  the  atmosphere.  In  this  manner  we  may  ascertain  the 
weight  of  a  column  of  air,  whatever  be  its  height. 

We  have  to  thank  the  mechanicians  of  Florence  for  the  first 
germ  of  the  discovery  of  this  important  law.  On  trying  to  raise 
water  above  thirty-two  feet  in  a  suction  pipe,  they  found  to  their 
great  surprise  that  the  fluid  would  not  rise  beyond  that  altitude. 
The  rising  of  a  fluid  was  explained  at  the  time  by  saying  that 
Nature  abhors  a  vacuum;  but  this  reason  did  not  satisfy  Galileo, 
who,  on  hearing  of  the  observations  made  by  the  pump-makers, 
at  once  came  to  the  conviction  that  the  gravity  of  the  air  was  the 


MEASUREMENT    OF    ATMOSPHERIC    PRESSURE.  121 

true  cause  of  the  phenomenon.  His  pupil,  Torricelli,  gave  con- 
vincing proofs  of  the  truth  of  this  conjecture,  and  arrived  at  nearly 
the  following  results.  In  order  that  two  different  columns  of  fluid 
should  be  equipoised,  it  is  necessary  that  their  heights  must  be 
inversely  as  their  densities.  Mercury  weighs  nearly  fourteen 
times  as  much  as  water.  If,  now,  the  atmospheric  air  can  sup- 
port a  column  of  water  thirty-two  feet  in  height,  it  must  also, 
according  to  the  above  view,  be  able  to  sustain  a  column  of  mer- 
cury -f|,  that  is,  of  twenty-eight  inches  in  height.  The  experi- 
ment is  easily  made.  We  fill  with  mercury  a  glass  tube  of  about 
thirty  inches  in  length,  and  closed  at  one  end,  and,  holding  the 
finger  over  the  open  end,  invert  it.  If,  then,  we  plunge  the  end 
closed  by  the  finger,  into  a  vessel  with  mercury,  and  then  remove 
the  finger,  the  mercury  will  immediately  sink  some 
Fig.  95.  inches,  until  the  elevation  of  the  mercury  in  the  tube 
is  as  much  beyond  the  level  of  the  mercury  in  the 
vessel  as  follows  from  the  above  considerations. 
The  column  of  mercury  in  the  tube  is  to  be  regarded 
as  an  equipoise  to  the  pressure  of  the  atmosphere. 
This  apparatus  constitutes  the  barometer.  The 
vacuum  above  the  column  of  mercury  is  termed  the 
Torricellian  vacuum.  We  may  express  the  above 
results  more  correctly.  The  vertical  height  of  the 
level  s  in  the  tube  above  the  level  a  b  is  called  the 
height  of  the  barometer.  It  is  not  the  same  in  all 
places,  or  at  all  times.  In  the  vicinity  of  the  sea  it 
averages  76  centimetres,  or,  what  is  nearly  the 
same  thing,  28  Paris  inches.*  Such  a  column  of 
mercury,  with  a  base  of  1  square  centimetre,  has  in 
cubic  contents  76  cubic  centimetres.  As,  now,  1  cubic  centi- 
metre of  mercury  weighs  13.59  grammes,  the  pressure  of  the 
column  on  its  base  is  76  X  13.59  grammes  =  1,033  kilogrammes. 
The  column  of  atmospheric  air,  which  at  the  level  of  the  sea  rests 
upon  a  base  of  1  square  centimetre,  presses,  therefore,  on  its  sur- 
face with  a  weight  of  1,033  kilogrammes.!  We  may  carry  this 
computation  still  further,  and  determine  the  weight  of  the  whole 
mass  of  air  composing  the  atmosphere.  For  instance,  whatever 


Very  nearly  thirty  English  inches. — TR. 

This  is  equivalent  to  a  pressure  of  fifteen  pounds  on  1  square  inch. — TE. 
11 


122 


CONSTRUCTION    OF    THE    BAROMETER. 


number  of  cubic  centimetres  the   earth's   surface   contains,  so 
many  times  1,033  kilogrammes  does  the  mass  of  the  air  weigh. 
Fig.  96.  Construction  of  the  Barometer. — Barometers  have 

had  various  forms  given  to  them,  according  to  the 
several  uses  for  which  they  are  intended.  Fig.  96 
represents  the  ordinary  barometer,  consisting  of  a  tube 
which  is  curved  at  the  bottom,  and  terminates  in  a 
wide  vessel,  the  whole  being  secured  to  a  board. 
The  graduated  scale  is  generally  made  of  metal.  If 
the  vessel  be  somewhat  wide  in  comparison  with  the 
bore  of  the  tube,  the  oscillations  of  the  column  exer- 
cise but  little  influence  upon  the  level  of  the  mercury 
in  the  vessel,  so  that  in  cases  where  extreme  exacti- 
tude is  not  requisite,  this  level  may  be  regarded  as 
constant.  In  these  barometers,  which  cannot  be  used 
in  very  nice  observations,  the  scale  is  generally  con- 
fined to  the  upper  part  of  the  instrument. 

In  travelling,  the  syphon  barometer  of  Gay  Lussac 
is  almost  exclusively  made  use  of,  owing  to  the  accu- 
rate results  it  yields,  the  facility  of  observing  it,  and, 
above  all,  the  ease  with  which  it  can  be  carried. 

The  open  limb  has  only  a  capillary  aperture  of 
sufficient  size  to  admit  the  air  freely,  and  too  small 
to  allow  of  the  mercury  escaping.  We  may,  there- 
fore, invert  it,  without  fear  of  losing  the  mercury. 

In  these  barometers,  the  lower  surface  of  the  mer- 
cury which  is  exposed  to  the  pressure  of  the  atmo- 
spheric air  has  no  fixed  position.  The  zero  point  from 
which  the  height  of  the  column  of  mercury  must  be 
measured,  rises  and  falls.  For  the  sake  of  safe  and 
convenient  transportation,  the  syphon  barometer  is 
generally  fastened  into  a  wooden  case  (Fig.  97), 
forming  a  staff  or  rod  when  closed. 

Whatever  may  be  the  form  of  the  barometer,  cer- 
tain conditions  must  be  satisfied,  if  the  instrument  is 
to  give  the  exact  amount  of  atmospheric  pressure. 
The  height  of  the  column  of  mercury  must  admit  of 
being  accurately  measured,  which  can  only  be  done 
if  the  tube  be  in  a  perfectly  vertical  position.  The 
degrees  of  the  scale  are  either  marked  upon  a  slip  of 


Fig.  97. 


AMOUNT    OF    ATMOSPHERIC    PRESSURE.  123 

brass  inserted  in  the  board  to  which  the  tube  is  secured,  or  are 
engraved  upon  the  tube  itself. 

The  space  above  the  column  of  mercury  must  be  perfectly  free 
of  air.  The  only  way  of  effecting  this  object,  is  by  boiling  the 
mercury  in  the  tube,  and  thus  removing  all  particles  of  air  and 
moisture,  adhering  to  the  sides  of  the  glass.  This  process  is  one 
requiring  much  practice  and  skill.  We  may  detect  the  presence 
of  a  particle  of  air  in  the  Torricellian  vacuum  by  the  space  not 
becoming  entirely  filled  with  mercury  on  inverting  the  tube,  a 
little  bubble  of  air  remaining  in  that  case  at  the  top  of  the  tube. 
The  larger  the  volume  of  the  empty  space,  the  less  importance  is 
to  be  attached  to  the  defect. 

Finally,  the  mercury  must  be  perfectly  pure,  and  the  bore  of 
the  tube  not  too  small.  If  the  tube  be  too  narrow,  the  adhesion 
and  the  friction  of  the  mercury  exercise  so  important  an  effect 
upon  the  sides  of  the  glass,  that  the  column  of  mercury  often 
remains  standing  higher  or  lower  than  it  ought,  according  to  the 
height  of  the  pressure  of  the  air.  If  in  such  cases  we  strike  the 
barometer,  we  may  see  the  column  of  mercury  instantly  rise  or 
fall,  according  to  its  previous  position,  as  the  hindrance  to  the 
motion  has  been  overcome  by  the  blow. 

Of  the  fluctuations  of  the  barometer  dependent  upon  the 
changes  of  the  weather  we  will  speak  further. 

Amount  of  Atmospheric  Pressure. — We  have  already  mentioned 
what  must  be  the  amount  of  pressure  of  air  corresponding  to  760 
millimetres  (30  inches)  of  the  barometer.  In  the  same  manner 
the  amount  of  atmospheric  pressure  may  be  reckoned  at  every 
height  of  the  barometer.  The  results  are  given  in  the  following 
table:— 


124 


AMOUNT    OF    ATMOSPHERIC    PRESSURE. 


Height  of  the 
Column  of 
Mercury. 

Pressure  upon 
One  Square 
Metre. 

Height  of  the 
Column  of 
Mercury. 

Pressure  upon 
One  Square 
Metre. 

Millimetres. 

Kilogrammes. 

Millimetres. 

Kilogrammes. 

500 

6793 

650 

8381 

510 

6929 

660 

8967 

520 

7065 

670 

9105 

530 

7201 

680 

9238 

540 

7336 

690 

9374 

550 

7472 

700 

9510 

560 

7608 

710 

9646 

570 

7744 

720 

9782 

580 

7880 

730 

9918 

590 

8016 

740 

10054 

600 

8152 

750 

10189 

610 

8287 

760 

10330 

620 

8423 

770 

10461 

630 

8559 

780 

10597 

640 

8695 

790 

10733 

The  surface  of  the  human  body  measures  about  2000  square 
inches ;  we  see,  therefore,  from  these  calculations,  the  enormous 
pressure  we  constantly  have  to  sustain,  and  yet  we  do  not  feel  it, 
owing  to  its  acting  uniformly  on  all  sides,  and  because  the  air 
within  our  bodies  perfectly  equipoises  the  external  pressure.  On 
the  summit  of  Mount  d'Or,  the  barometric  column  is  only  600 
millimetres  (23.5  inches);  a  weight  of  2,173  kilogrammes  (about 
4,650  Ibs.)  is,  therefore,  gradually  removed  from  the  traveller  as  he 
ascends  higher  and  higher  up  the  mountain,  and  still  more  on 
reaching  the  summit  of  Mount  Etna  or  Lebanon.  The  diminished 
pressure  of  the  air  at  higher  elevations  produces  the  most  peculiar 
effects  upon  the  human  body,  which  is  not  made  to  endure  so 
rarefied  a  state  of  the  atmosphere.  Even  persons  in  good  health 
experience  lassitude,  indisposition  and  oppression. 

[This  decrease  in  the  density  of  the  atmosphere,  as  we  ascend 
above  the  surface  of  the  earth,  is  very  rapid :  thus,  at  an  elevation 
of  3  miles,  the  pressure  of  the  air  is  only  \  of  that  at  the  level  of 
the  sea;  at  6  miles  J;  at  9  miles  \\  and  at  15  miles  ^V;  this  is 
shown  by  the  subsidence  of  the  mercury  at  the  several  eleva- 
tions. 


PUMPS. 


125 


At  the  level  of  the  sea,  it  stands  at 
At    5,000  feet  elevation 
"  10,000          «  . 

"  15,000 

"     3  miles  .... 
"     6     " 
"     9     "      . 
"  15     " 


30         inches. 
24.797     " 
20.499     " 
16.941      « 
15.000     « 
7.50       « 
3.75       " 
1.00       «  ] 

Pumps. — A  number  of  phenomena,  of  which  we  are  daily  wit- 
nesses, admit  of  being  explained  by  the  pressure  of  the  air.  If 
we  suck  the  upper  end  of  a  tube  immersed  in  water,  the  liquid 
will  rise  in  the  interior  of  the  tube,  owing  to  the  air  in  the  upper 
part  being  rarefied  by  the  action  of  sucking,  and  the  pressure  of 
air  acting  on  the  external  level  of  the  water  forcing  the  liquid 
into  the  tube.  We  may  produce  a  similar  rising  of  the  water  by 
inserting  a  piston  in  the  interior  of  the  tube,  by  the  working  of 
which  the  air  will  be  likewise  rarefied.  Upon  this  principle  de- 
pends the  construction  of  pumps. 

The  Suction  Pump  consists  of  a  suction  or  feeding  pipe  a  (Fig. 
98),  a  cylinder  6,  a  piston  p,  an  upper  pipe 
s,  and  three  valves  r,  t  and  /,  opening  up- 
wards. The  valve  r  is  at  the  bottom  of  the 
cylinder,  t  is  in  the  piston,  and  /  in  the 
lower  end  of  the  upper  pipe.  The  suction- 
pipe  plunges  into  the  wTater  we  wish  to  raise, 
and  the  piston-rod  moves  air-tight  through 
the  box  e.  When,  on  the  first  movement, 
the  piston  is  raised,  t  closes,  but  r  and  /  are 
open:  /  owing  to  the  condensation  of  air 
above  the  piston,  and  r  owing  to  its  rarefac- 
tion below  the  piston.  As  the  pressure  of 
air  in  the  suction-pipe  diminishes,  the  water 
rises  in  consequence  of  the  preponderance 
of  the  external  pressure.  The  lower  valve 
closes  as  the  piston  descends.  The  air  in 
the  cylinder  below  the  piston  is  compressed, 
and,  opening  the  valve  £,  passes  through  the  piston  into  the  upper 
part  of  the  cylinder.  On  the  second  elevation  of  the  piston,  the 
water  again  ascends  higher  in  the  suction-pipe,  while  a  quantity 
of  air  is  again  expelled  through  the  valve  I.  At  last,  after  a  cer- 

11* 


126  HYDROSTATICS. 

tain  number  of  strokes  of  the  piston,  the  water  ascends  above  the 
valve  r  and  lifts  up  the  valve  t.  Then,  all  the  air  being  expelled 
from  the  pump,  every  valve  is  raised  by  the  water  alone.  Every 
time  the  piston  descends,  a  quantity  of  water  passes  through  the 
valve  t,  and  at  each  stroke  a  fresh  supply  is  raised  into  the  upper 
pipe  and  the  suction-pipe.  The  force  expended  in  raising  the 
piston  is  partly  lost  in  overcoming  the  friction,  and  in  counteract- 
ing the  pressure  of  a  column  of  water  wrhose  base  is  equal  to  the 
surface  of  the  piston,  and  whose  height  is  equal  to  the  vertical 
distance  between  the  orifice  at  which  the  water  escapes,  from  the 
upper  tube  over  the  level  of  the  liquid,  into  which  the  suction- 
pipe  is  immersed.  To  make  a  pump  efficient,  the  water  must  be 
able  to  reach  the  first  valve  r.  The  position  of  this  valve  depends 
upon  the  degree  of  rarefaction  which  can  be  produced  between 
the  valves  t  and  r.  If  there  were  no  space  between  r  and  t  at 
the  lowest  position  of  the  piston,  an  absolute  vacuum  might  be 
produced  between  these  two  valves,  and  the  valve  r  should  be 
placed  thirty-two  feet  above  the  level  of  the  water  of  the  reservoir. 
But,  as  it  is  impossible  entirely  to  avoid  interstices  occurring 
below  the  piston,  the  valve  r  must  not  be  elevated  quite  thirty- 
two  feet  above  the  level  of  the  reservoir.  Care  must,  however, 
be  taken  to  make  the  space  as  small  as  possible  in  comparison 
with  the  contents  of  the  cylinder.  If,  for  example,  the  space 
occupied  one  half  of  the  contents  of  the  cylinder  (excepting  that 
filled  by  the  piston),  we  could  only  rarefy  the  air  between  r  and  t 
to  half  the  pressure  of  the  atmospheric  air,  and  consequently  the 
valve  r  should  not  be  elevated  more  than  sixteen  feet  above  the 
level  of  the  water  in  the  reservoir. 

The  Suction  and  Forcing  Pump  (Fig.  99) 
Flg*     '(|  consists  of  a  suction-pipe  a,  an  upper  pipe  s, 

a  cylinder  c,  and  a  heavy  piston  p ;  it  has  only 
two  valves,  r  and  /.  On  raising  the  piston, 
the  water  forces  itself  through  the  valve  r\  on 
lowering  the  piston,  r  is  closed,  and  the  water 
raised  up  is  forced  through  /. 

The  Syphon. — If  we  fill  a  drinking  glass 
having  a  smooth  edge  (cut  glass  is  the  best) 
with  water,  cover  it  with  a  paper,  and  invert 
it,  the  water  will  not  run  out,  the  pressure  of 
the  air  acting  on  the  under  surface  of  the  paper, 


COMMON    SYPHON. 


127 


and  thus  hindering  the  escape  of  the  liquid.  The  paper  is  only 
so  far  necessary,  as  to  enable  us  to  invert  the  glass,  and  Fi  I0a 
prevent  the  water  from  running  out  at  the  sides,  and  air- 
bubbles  entering  the  vessel.  When  the  lower  opening 
is  so  small  as  to  leave  no  fear  of  the  liquid  thus  running 
out,  as  is  the  case  with  the  form  of  syphon  depicted  in 
Fig.  100,  the  paper  is  unnecessary.  This  syphon  is  a 
common  tubular  vessel,  constricted  above  and  below, 
and  open  at  both  extremities.  If  we  plunge  it  entirely 
into  a  liquid  when  both  orifices  are  open,  it  will  be  en- 
tirely filled,  and  placing  the  thumb  over  one  opening,  we 
may  lift  the  syphon  up  without  any  of  the  fluid  contained 
in  it  escaping. 

The  common  syphon  (Fig.  101)  is  a  curved  tube,  b  s  b'9  whose 
legs  are  of  unequal  length.  If  the 
shorter  leg  be  plunged  into  a  liquid, 
and  the  whole  tube  filled,  the  liquid 
will  continue  to  run  out  at  b',  the  end 
of  the  longer  leg  lying  lower  than  b ; 
we,  may,  therefore,  easily  empty  a 
vessel  by  means  of  a  syphon.  The 
action  of  the  syphon  admits  of  a  ready 
explanation.  On  the  one  side  the 
column  of  water  s  bf,  and  on  the  other 
the  column  of  water  from  s  to  the  level 

of  the  liquid  in  the  vessel,  have  a  tendency  to  fall,  owing  to  their 
gravity. 

The  gravity  of  the  two  columns  of  water  in  the  different  legs 
is,  however,  opposed  on  both  sides  by  the  pressure  of  air  acting 
on  the  one  side  on  the  aperture  &',  but  on  the  other  on  the  sur- 
face of  the  water  in  the  vessel,  and  thus  hindering  the  formation 
of  a  vacuum  in  the  interior  of  the  tube,  which  would  necessarily 
be  formed  at  s  if  the  columns  of  water  ran  down  on  both  sides. 

As  the  pressure  of  air  acts  alike  strongly  on  both  sides,  equili- 
brium would  be  established  if  the  columns  of  water  were  equally 
high  in  the  two  legs;  that  is,  if  the  opening  b'  were  at  the  eleva- 
tion of  the  level  of  the  water  in  the  vessel ;  as  soon,  however,  as 
b'  lies  deeper,  the  column  in  the  leg  s  b'  preponderates,  and,  in 
proportion  as  the  water  escapes  there,  water  is  again  forced  into 
the  tube  on  the  other  side  by  the  pressure  of  the  air,  so  that  the 


128 


HYDROSTATICS. 


Fig.  102. 


Fig.  103. 


liquid  continues  to  escape  until  the  level  of  the  water  in  the  vessel 
has  fallen  to  the  height  of  the  opening  bf,  or  the  opening  at  b  has 
been  set  free. 

A  suction-tube,  a  t  (Fig.  102),  is  sometimes  attached  to  the 
syphon  to  make  it  more  useful  and  efficient.  We 
fill  a  common  syphon  by  sucking  at  b' ;  as  this  pro- 
cess, however,  is  objectionable,  owing  to  the  diffi- 
culty of  preventing  the  fluid  from  entering  the 
mouth,  which  might  be  very  dangerous  in  some 
cases,  as,  for  instance,  in  emptying  a  vessel  of  sul- 
phuric acid,  a  suction-tube  is  indispensably  neces- 
sary,  as,  by  means  of  this,  we  may  fill  the  whole  leg 
s  bf  by  sucking  at  t,  without  the  fluid  entering  the 
mouth,  if  we  close  the  tube  at  b'.  The  escape  of 
the  fluid  begins  as  soon  as  we  again  open  the  end 
b'  of  the  tube. 

Mariotte's  Law.     The  volume  of  gases  is  inversely  proportional 
to  the  pressure  to  which  they  are  subjected. — To  prove  this  funda- 
mental law  by  experiment,  we  take  a  curved  cylin- 
drical tube  whose  shorter  leg  is  closed  above,  while 
the  longer  one  remains  open. 

At  first  we  pour  a  little  mercury  into  the  tube, 
and  then  incline  it  somewhat  that  the  air  may  escape 
from  the  shorter  leg.  By  this  means  we  can  easily 
contrive  that  the  mercury  shall  stand  equally  high 
in  both  legs.  Then  the  air  enclosed  in  the  space  a  b 
(Fig.  103)  is  exactly  counterpoised  by  the  pressure 
of  the  atmosphere.  If  we  again  pour  mercury  into 
the  open  leg,  the  pressure  to  be  sustained  by  the 
enclosed  air  is  increased,  and  the  latter  is  compressed 
within  a  smaller  space.  If  the  mercury  rise  in  the 
shorter  leg  to  the  point  m,  half  way  between  a  and  6, 
the  air  will  be  compressed  to  the  half  of  its  former 
volume ;  if  now  we  mark  on  the  longer  leg  the  point 
n  at  an  equal  height  with  m,  and  measure  how  high 
the  mercury  has  risen  above  n  in  the  longer  leg,  we 
shall  find  that  the  height  of  the  column  of  mercury 
s  n  is  exactly  equal  to  the  height  of  the  barometer; 
the  air  enclosed  in  b  m  has,  therefore,  to  support  the  pressure  of 
two  atmospheres.  If  the  open  leg  of  this  apparatus  were  long 


MARIOTTE'S    LAW. 


129 


Fig.  104. 


enough,  we  might  show  in  the  same  manner  that  a  pressure  of 
three  or  four  atmospheres  would  compress  the  enclosed  air  to 
one-third  or  one-fourth  of  its  original  volume.  Arago  and  Dulong 
have  shown  that  for  atmospheric  air  this  law  does  not  vary  in  its 
application  at  least  up  to  a  pressure  of  twenty-seven  atmospheres. 

By  this  experiment  the  correctness  of  Mariotte's  law  is  proved 
from  the  pressure  of  one  atmosphere  to  the  pressure  of  twenty- 
seven  atmospheres;  while  for  a  pressure  of  less  than  one  atmo- 
sphere we  may  confirm  the  principle  by  the  help  of  the  apparatus 
about  to  be  described  (Fig.  104).  A  somewhat  wide  glass  tube, 
terminating  above  in  a  wider  vessel,  and  closed  below,  .is  so 
placed  in  a  frame  as  to  stand  vertically.  It  is  filled 
with  mercury  to  about  the  line  c  n.  We  now  fill  a 
barometer-tube  (as  in  the  Torricellian  experiment 
before  described)  with  mercury,  leaving,  however,  a 
space  of  an  inch  to  two  inches  empty.  If  we  now 
close  the  aperture  with  the  finger,  and  invert  it,  the 
air-bubble  will  ascend  into  the  upper  part  of  the 
tube. 

If,  now,  as  in  the  Torricellian  experiment,  the  lower 
end  of  the  tube  enters  the  mercury  of  the  vessel  en, 
and  we  remove  the  finger  from  the  tube,  the  column 
of  mercury  in  the  barometer-tube  will  fall  to  a  certain 
point.  But  we  shall  immediately  observe  that  the 
summit  of  the  column  of  mercury  does  not  stand  so 
high  above  c  n  as  the  barometric  height  measures, 
because  there  is  air  in  the  upper  part  of  the  tube, 
and  no  vacuum  as  in  the  barometer. 

If  we  press  down  the  tube  until  it  reaches  further 
and  further  into  the  mercury  of  the  wide  tube,  the 
volume  of  the  enclosed  air  will  become  smaller.  We 
now  press  the  tube  so  far  down  that  the  mercury  in 
the  tube  stands  exactly  at  the  height  of  the  level  of 
the  mercury  en.  In  this  case  the  enclosed  air  is 
submitted  exactly  to  the  pressure  of  one  atmosphere. 

The  height  of  the  enclosed  column  of  air  exposed  to  the  pres- 
sure of  one  atmosphere  is  now  measured:  it  amounts  to  1.96 
inch. 

If  we  again  draw  up  the  tube,  the  volume  of  air  increases,  but 
at  the  same  time  the  top  of  the  mercury  rises  above  the  level  en. 


130  HYDROSTATICS. 

Provided  we  draw  the  tube  so  far  up,  that  the  enclosed  air  occupies 
a  length  of  ten  centimetres  (3.93  in.)  in  the  tube,  the  height  of 
the  top  of  the  mercury  above  the  level  en  will  be  exactly  half  of  the 
height  of  the  barometer  observed  at  the  moment.  For  instance,  if 
the  barometer  stand  at  760  millimetres,  (30  inches,)  the  top  of  the 
mercury  will  be  exactly  380  millimetres  (15  inches)  above  en. 

The  half  of  the  atmospheric  pressure  is,  therefore,  counterba- 
lanced by  the  column  of  mercury  under  the  enclosed  air,  and  the 
pressure  which  the  latter  has  to  sustain  is  only  equal  to  the  pres- 
sure of  half  the  atmosphere ;  its  volume,  however,  is  twice  as  large 
as  it  was  when  supporting  the  pressure  of  one  atmosphere.  If,  now, 
we  raise  the  tube  so  far  that  the  enclosed  air  occupies  a  length  of 
fifteen  centimetres,  (5.89  inch,)  so  that  its  volume  is  three  times 
greater  than  it  was,  the  height  of  the  column  of  mercury  in  the 
tube  amounts  to  two-thirds  of  the  barometric  height :  the  enclosed 
air  has,  therefore,  only  a  pressure  of  one-third  of  an  atmosphere 
to  sustain. 

Measurement  of  heights  by  the  Barometer. — If  the  air  were  not 
an  elastic  fluid,  but  were  like  water,  it  would  be  extremely  easy 
to  compute  heights  by  the  barometer.  At  the  level  of  the  sea,  the 
barometer  stands  at  760mm,  as  soon  as  we  ascend  11, 5  metres,  the 
barometer  falls  to  759ram;  a  column  of  air  of  11,5  metres  in 
height  will,  therefore,  equipoise  a  column  of  mercury  of  lmm  in 
height. 

From  this  we  may  calculate  the  density  of  the  air,  for  it  is  to 
that  of  mercury  as  lmm  is  to  11,5™,  or  as  1  to  11500,  that  is,  the 

density  of  the  air  is th  of  that  of  mercury.    The  density  of 

11500 

1  O  CZ. 

the  air  is,  therefore,         '    ,  or  nearly  0,0012  that  of  water,  since 
11500 

water  is  13,6  times  lighter  than  mercury.  If,  now,  the  air  were 
like  water,  the  density  of  the  strata  of  air  lying  above  us  would 
be  equally  great,  and  we  should  then  only  have  to  ascend  11,5 
metres  to  have  the  barometer  again  to  fall  lmm ;  and  if,  by  con- 
tinued ascent,  the  barometer  had  fallen  n  millimetres,  we  should 
then  have  attained  a  height  n  x  1 1,5  metres.  But  the  air  is  elastic  ; 
the  smaller  the  pressure  weighing  upon  it,  the  less  will  be  its 
density ;  consequently,  the  higher  we  ascend,  the  more  rarefied  is 
the  air. 

The  law  by  which  the  density  of  the  air  diminishes  by  constant 


MEASUREMENT    OF    HEIGHTS.  131 

ascent,  and  the  relations  existing  between  the  height  of  the  baro- 
meter and  elevations  above  the  soil,  can  be  developed  by  Ma- 
riotte's  law. 

Suppose  the  barometer  to  stand  at  760mra  at  any  given  spot.   If 
we  ascend   11,5  metres,  the  barometer  will  fall   to  759mm,  or 

what  is  the  same  thing  760  — .     Without  any  serious  error,  we 

760 

may  assume  that  the  whole  layer  of  air  everywhere  at  a  height 
>f  11,5  metre,  is  of  equal  density  with  that  at  the  level  of  the  sea. 
n  Fig.  105,  a  is  a  point  on  the  earth's  surface,  b  is  a  point 
ying  11, 5m  higher,  and  each  one  of  the  several  points  c,  d, 
e,  &c.,  is  11, 5m  above  the  lower  one.  As  the 
density  of  the  air  is  proportionate  to  its  pressure, 
the  layer  b  c  is  less  dense  than  the  layer  a  b, 
and  the  densities  of  these  layers  will  be  as  the 
height  of  the  barometer  at  a  and  b;  that  is,  the 

• — 

e  layer  a  b. 

If,  now,  we  ascend  from  b  to  c,  the  barometer 


h  ' '    7^(76b)    Density  °f  ^e  layer  b  c  is  . —   of  the  density  of 

g 
f 


G59v  5 
_\  7(^Qram 

60J   does  not  fall  so  much  as  lmm,  but  only  _     .The 

/759x4  760 

\76oj    height  at  which  the  barometer  stands,  is,  there- 


-,™/759\3  f        -Cfl759mm      759      7592       -~A  /759\2 
760(7TO)    fore,  760  _    -  -  =  _  =  760  (_) . 

c  |    76o(^Vln  this  manner  we  may  further  conclude  that 
'    the  densities  of  the  layers  b  c  and  c  d  are  as  the 

/759\  ! 

b  •  •    760  ( ~^-n)    heights  of  the  barometer  b  and  c,  and  that  conse- 


a        760  quently  the  layer  c  d  is times   lighter   than 

760 

the  layer  b  c.     If,  therefore,  the  layer  b  c  could  support  a  column 

759mm 

of  mercury  of  —     ,  the  layer  c  d  can  only  bear  a  column  of 
760 


_x:rr=(^:r)    millimetres;   and  if  we  rise  from  c  to  d,  the 
760    760     \760/ 

barometer  must  fall  ( — \    millimetres.  At  d,  likewise,  the  height 
of  the  barometer  is  760  ( j   — 


132 


HYDROSTATICS. 


It  will  easily  be  understood  that  formulae  may  be  constructed 
from  these  considerations,  by  the  aid  of  which  the  difference  of 
height  of  two  places  may  be  computed,  if  the  height  of  the  baro- 
meter be  accurately  measured  at  both  places. 

The  Mr  Pump  must  be  ranked  amongst  the  most  indispensable 
and  important  instruments  of  the  Natural  Philosopher,  and  has 
undergone  many  alterations  and  improvements  since  its  invention 
by  Otto  von  Guericke.  We  will  now  consider  it  in  its  most  simple 
form,  in  the  small  air  pumps  which  are  at  present  used  in  all 
chemical  laboratories. 

We  must  suppose  a  hollow  cylinder,  perfectly  closed  below,  and 
having  a  piston  c  closely  fitting  to  the  bottom.  If  now  the  piston 
be  forcibly  drawn  up,  a  vacuum  is  formed  below  it,  provided  the 
friction  be  air  tight  against  the  sides  of  the  cylinder. 
Nothing,  however,  can  be  done  by  means  of  this 
vacuum  since  we  can  neither  see  into  it,  nor  put 
anything  within.  But  if  a  canal  lead  from  the 
lower  part  of  the  cylinder  into  a  sphere,  a  balloon 
e,  for  instance,  which,  although  filled  with  air,  is 
fully  closed  against  the  external  atmosphere,  a  por- 
tion of  the  air  in  e  will  enter  the  cylinder,  owing  to 
its  elasticity,  on  lifting  up  the  piston,  and  a  rarefac- 
tion of  the  air  in  e  will  consequently  follow.  In 
order,  however,  that  the  air  may  not  return  into  e  on 
the  descent  of  the  piston,  a  cock  s  is  attached  by  means  of  which 
the  communication  between  e  and  the  cylinder  maybe  interrupted, 
or  again  restored  at  will.  This  cock  s  is  closed  as  soon  as  the 
piston  comes  over  it.  If  we  now  press  down  the  piston,  the  air 
in  the  cylinder  will  only  be  compressed,  if  we  afford  it  no  means 
of  escape  ;  this,  however,  it  will  have,  if  we  open  a  second  cock  t. 
When  the  piston  is  at  the  bottom,  t  is  again  closed,  and  s  opened, 
while  another  drawing  up  of  the  piston  produces  another  rarefac- 
tion in  e.  By  frequent  repetition  of  this  operation,  we  may  obtain 
a  considerable  rarefaction  at  e. 

The  apparatus  in  this  form  is,  however,  inconvenient 
on  many  accounts.  In  the  first  place,  the  continual 
opening  and  shutting  of  the  two  cocks  is  extremely  trou- 
blesome. But  for  the  cock  t  we  may  substitute  a  valve 
which  closes  on  the  elevation,  and  opens  on  the  de- 
pression of  the  piston.  The  lower  part  of  the  piston 


AIR   PUMP. 


133 


Fig.  109. 


consists  of  a  brass  plate,  with  a  screw  screwed  into  Fis-  108- 
a  piece  of  brass  c  c.  The  screw  is  perforated  along 
its  length,  and  a  piece  of  silk  r  bound  over  the  open- 
ing o.  In  the  piece  of  brass  to  which  the  screw  is 
fixed,  there  is  an  opening  b.  On  the  elevation  of 
the  piston,  the  air  in  the  upper  part  of  the  cylinder 
forces  itself  through  the  opening  b  in  the  silk,  and 
presses  it  tightly  upon  the  opening  o ;  the  piston  acts,  therefore, 
on  rising,  exactly  as  if  it  were  solid:  the  air  passes  from  the 
space  e  through  the  open  cock  s  into  the  lower  part  of  the  cylin- 
der ;  but  if,  after  the  cock  s  is  closed,  the  piston  be  again  pressed 
down,  the  air  in  the  under  part  of  the  cylinder  will  be  compressed, 
and  raising  the  valve  r,  will  escape  through  the  opening  b  into  the 
upper  part  of  the  cylinder. 

The  piece  of  brass  c  is  inserted  into  a  cork  bound  round  with 
fine  leather.  This  leather  is  pressed  against  the  sides  of  the 
cylinder  by  the  elasticity  of  the  cork. 

The  cock  s  may  also  be  dispensed 
with,  if  a  second  valve  be  applied  to 
the  part  where  the  canal  opens  into  the 
cylinder.  This  valve  opens  on  draw- 
ing up  the  piston,  and  closes  with  its 
descent.  The  accompanying  figure 
shows  a  very  useful  little  air-pump,  one- 
third  of  the  natural  size.  It  has  been 
constructed  in  accordance  with  the  plan 
of  Gay  Lussac.  The  canal  goes  ver- 
tically down  from  the  lower  end  of  the 
cylinder  into  a  canal  a  b  running  hori- 
zontally. The  cork  at  d  should  be 
closed,  and  the  receiver  from  which  the 
air  is  to  be  exhausted,  screwed  on  at  a; 
then  on  raising  the  piston,  a  portion  of 
the  air  will  pass  first  through  the  hori- 
zontal, and  then  through  the  vertical 
canal  into  the  cylinder,  and  on  pressing 
down  the  piston,  will  escape  through  its 
valve.  To  admit  the  air  again  into  the 
receiver,  nothing  more  is  necessary  than  to  open  the  cock  at  d. 

By  means  of  the  screw./,  the  air  pump  my  be  screwed  on  to  a 
12 


134 


AIR    PUMP. 


table,  or  to  a  board  secured  to  a  table,  and  will  thus  remain 
fixed  while  being  used. 

We  designate  by  the  term  receiver,  the  space  from  which  the 
air  is  to  be  exhausted.  The  best  form  for  receivers  of  air  pumps, 
designed  for  general  experiments,  is  a  bell  made  of  glass,  the 
under  and  somewhat  broader  edge  of  which  must  be  made  per- 
fectly smooth  and  polished,  so  that  it  may  fit  into  a  smoothly  cut 
plate  with  such  exactitude  as  to  prevent  the  entrance  of  any  air 
between  the  two.  A  perfect  exclusion  can,  however,  only  be 
effected  by  rubbing  the  edge  of  the  bell  with  tallow  before  placing 
it  upon  the  plate.  In  Fig.  110  we  see  a  receiver  of  this  kind  in 

conjunction    with     a 

Fi§-  no-  little  air  pump.  From 

the  middle  of  the  plate, 
a  canal  goes  verti- 
cally down  and  then 
passes  further  on 
through  a  short  hori- 
zontal tube.  At  the 
end  of  this  short  hori- 
zontal piece  of  tube,  a 
glass  tube  is  attached 
by  means  of  an  India- 
rubber  tube,  and  is 
secured  in  a  similar 
manner  to  the  air- 
pump  on  the  opposite  side.  The  degree  of  rarefaction  that  can 
be  obtained  by  pumping,  may  be  measured  by  what  is  termed  the 
barometric  test.  This  is  applied  to  the  smaller  air  pumps  in  the 
manner  shown  at  Fig.  110.  A  glass  tube  of  about  thirty  inches 
in  length  is  immersed  at  its  lower  end  into  a  vessel  full  of  mer- 
cury. 

Above  it  is  curved,  and  secured  to  the  pump  by  means  of  a 
short  but  wider  piece  of  tube.  If  the  cock  d  be  opened,  the  mer- 
cury will  ascend  in  the  tube  in  proportion  as  the  rarefaction  is 
continued.  If  it  were  possible  to  create  a  perfect  vacuum  by 
means  of  the  air  pump,  the  column  of  mercury  raised  in  the  tube 
e,  would  be  equal  to  the  height  of  the  barometer. 

With  a  well  constructed  apparatus  of  this  kind,  we  may  make 
most  of  the  experiments  of  the  air  pump,  with  the  exception  per- 


AIR   PUMP. 


135 


Fig.  Ill, 


\c 


haps  of  some  few,  requiring  very  large  receivers,  or  a  very  rapid 
and  complete  exhaustion.  On  this  account,  air  pumps  of  this 
kind  are  to  be  recommended  for  all  popular  institutions,  not  pos- 
sessing the  funds  necessary  to  obtain  the  more  highly  finished 
apparatus,  viz.,  when  they  are  made  four,  five,  or  six  times  larger 
than  the  one  represented  in  Fig.  109. 

Larger  air  pumps  of  various  forms  have  been  constructed,  but 
all  are  based  upon  the  same  principles  as  the  ones  above  described. 
We  will  consider  more  attentively  one  of  the  best  arranged  of 
these  apparatuses. 

In  a  cylinder  «,  which  must  be  perfectly  well  finished,  the  piston 
b  moves  by  means  of  the 
rod  c,  which  must  be  per- 
fectly air-tight,  no  air  be- 
ing able  to  escape  between 
the  piston  and  the  cylin- 
der. 

In  the  piston  there  is  a 
valve  5,  which  must  move 
easily,  and  open  up- 
wards. It  rises  when  the 
pressure  from  below  is 
greater  than  from  above, 
but  otherwise  remains  her- 
metically closed. 

The  rod  e  d  is  the  valve  for  the  cylinder.  If  the  piston  be 
raised,  the  whole  rod  is  lifted  up,  but  d  soon  strikes  the  upper 
plate  of  the  cylinder,  and  the  piston  moves  with  some  friction 
along  the  whole  rod.  As  soon  as  the  piston  descends,  the  trun- 
cated cone  e  is  pressed  into  the  conical  opening  below  it,  so  that 
the  upper  surface  of  the  cone  e,  and  the  bottom  of  the  cylinder 
form  a  plane  surface,  and  the  piston  may,  therefore,  rest  perfectly 
on  this  bottom. 

From  the  above-mentioned  conical  opening,  a  canal  goes  on  to 
v.  Here  there  is  a  screw,  to  wrhich  may  be  attached  the  balloons 
or  receivers  that  are  to  be  exhausted. 

The  screw  v  is  in  the  middle  of  a  plate  p,  on  which  the  bell  h 
may  be  placed.  Let  us  assume  that  the  piston  is  on  the  lower 
plate  of  the  cylinder.  If  then  it  be  raised,  a  vacuum  will  be 
formed,  provided  all  the  valves  remain  shut ;  but  the  valve  e  is 


136  BAROMETRIC    GAUGE. 

opened,  and  the  air  from  the  bell  passes  partly  over  to  the  cylin- 
der. 

But  by  this  means,  the  air  in  the  bell  and  in  the  canal  of  the 
bell  is  rarefied,  consequently  the  valve  s  in  the  piston  must  remain 
closed.  On  the  descent  of  the  piston,  the  valve  at  e  is  shut,  and 
all  passage  closed  for  the  return  of  the  air  from  the  cylinder  into 
the  bell.  The  air  thus  shut  in  will  escape  through  the  valve  s,  until 
the  piston  reaches  the  bottom  of  the  cylinder.  Another  upward 
stroke  of  the  piston  produces  a  fresh  rarefaction  in  the  bell. 

We  may  easily  understand  that  an  absolute  vacuum  can  never 
be  produced  in  this  manner  below  the  bell,  however  long  we  may 
continue  the  above-mentioned  operation,  because  by  every  fresh 
stroke  of  the  piston,  the  air  below  the  bell  is  only  re-rarefied;  we 
may,  however,  easily  manage  to  reduce  the  air  until  it  has  only 
a  tension  of  two  millimetres.  The  time  required  to  produce  a 
certain  degree  of  rarefaction  wil!4be  shorter  or  longer,  according  to 
whether  the  volume  of  the  receiver  be  small  or  large  in  compa- 
rison with  the  volume  of  the  cylinder. 

If  we  have  exhausted  the  pump  sufficiently,  the  atmospheric 
pressure  acting  upon  the  piston  is  not  counterpoised  by  any  oppo- 
site pressure  within.  In  order  to  raise  the  piston,  we  must  apply 
a  force  of  1033  kilog.  for  every  square  centimetre  of  its  surface, 
besides  having  to  overcome  the  friction. 

In  air  pumps  with  two  cylinders,  the  pressure  on  the  one  piston 
acts  against  that  weighing  down  the  other  piston,  and  thus  nothing 
but  friction  remains  to  be  overcome. 

In  the  canal  connecting  the  receiver  with  the  sucker,  a  double- 
Fi  H2  acting  cock  y  is  applied;  that  is  to  say, 

a  cock  having  two  openings,  a  common 
straight  aperture  connecting  the  receiver 
with  the  sucker,  while  the  pump  is  being 
worked,  and  a  lateral  opening  closed  by  a  metal  stopper  5,  and 
turned  towards  the  sucker,  when  the  receiver  is  to  be  shut  off. 
If  we  wish  to  let  air  again  into  the  receiver,  we  must  turn  the 
cock  in  such  a  manner  that  the  lateral  opening  is  turned  to  the 
receiver,  and  then  draw  out  the  metal  stopper. 

In  these  air  pumps,  the  barometric  gauge  is  generally  differently 
constructed  from  the  above-mentioned.  It  is  usually  a  shortened 
barometer,  closed  in  a  long  narrow  bell  r,  Fig.  Ill,  and  con- 
nected with  the  canal  of  the  machine.  This  connection  may  be 


AIR   PUMP. 


137 


cut  off,  or  again  restored  by  means  of  a  cock.  Fig.  113  repre- 
sents an  isolated  barometer  gauge,  seven  inches  in  length.  Fig.  us. 
The  mercury  entirely  fills  the  closed  leg,  and  only  begins 
to  sink,  when  the  pressure  of  air  acting  on  the  open  leg 
is  reduced  to  one-fourth  of  the  atmospheric  pressure.  If 
this  degree  of  rarefaction  be  obtained,  the  barometric  test 
will  always  give  the  pressure  of  the  air  in  the  receiver, 
which  is  equal  to  the  difference  of  the  height  of  the  two 
columns  of  mercury.  As  soon  as  air  is  again  admitted, 
its  pressure  will  drive  the  mercury  forcibly  back  into  the 
closed  tube;  we  must,  therefore,  moderate  the  rush  of 
air  to  prevent  the  top  of  the  glass  tube  from  being  broken 
through. 

Otto  von  Guericke  made,  by  means  of  the  machine  which  he 
constructed,  the  remarkable  experiment  with  the  Magdeburg 
Hemispheres,  which  consisted  in  producing  a  vacuum  in  a  hollow 
metal  ball,  the  halves  of  which  were  only  simply  laid  on  each 
other.  Before  the  vacuum  is  formed,  it  is  easy  to  separate  the 
parts,  but  when  they  have  been  entirely  exhausted  of  air,  and 
there  is  nothing  to  counteract  the  external  atmospheric  pressure, 
they  adhere  most  extraordinarily  close  together.  If,  for  instance, 
the  radius  of  the  ball  were  only  1  decimetre, 
a  section  through  its  centre  would  be  314 
square  centimetres,  and  consequently  the  ex- 
ternal pressure  holding  the  two  halves  toge- 
ther would  be  more  than  314  kilogrammes. 
[In  other  words,  they  will  be  pressed  together 
by  as  many  15  pounds  as  there  are  square  inches  of  surface.] 

Fig.  115. 


Fig.  114. 


138  AIR    PUMP. 

In  order  to  make  the  contact  more  perfect,  the  edges  of  the 
hemispheres  are  rubbed  with  fat,  like  the  bell  before  it  is  placed 
on  the  plate ;  the  cock  c,  which  is  open  while  the  pumping  goes 
on,  is  closed  before  the  united  hemispheres  are  taken  off  the  air 
pump,  and  the  re-entrance  of  air  is  thus  prevented. 

The  air  pump  is  used  in  many  experiments.  By  this  means  it 
may  be  shown  that  burning  bodies  are  extinguished  in  a  vacuum ; 
that  smoke  falls  to  the  ground  like  a  heavy  body;  that  air,  as  it 
were,  is  dissolved  in  water ;  that  a  layer  of  air  intervenes  between 
fluids  and  the  sides  of  the  vessels  in  which  they  are  contained,  for 
its  presence  is  manifested  by  a  number  of  little  globules  that 
increase  in  proportion  as  the  air  diminishes.  By  the  aid  of  an  air 
pump,  we  may  cause  cold  water  to  boil. 

A  glass   cylinder  about  one  yard  in   height,  and   having  a 
116  diameter  of  about  eight  inches, 

whose  upper  and  lower  edges 
are  carefully  smoothed,  is 
placed  upon  the  plate  of  the 
air  pump ;  the  upper  aperture 
of  the  cylinder  is  closed  by  a 
metal  plate  (as  exhibited  in 
Fig.  116)  hermetically  attached 
to  the  polished  glass  edge  by  being  rubbed  with  fat.  Through 
the  middle  of  this  plate,  there  passes  an  air-tight  metal  cone 
(almost  like  a  cock),  that  may  be  turned  at  will.  Two  horizon- 
tally secured  rods  s  revolve  with  this  metal  cone. 

On  each  of  the  rods  there  is  a  little  metal  plate  t  fastened  to  a 
rod  projecting  from  the  metal  plate  by  means  of  a  horizontal  pin, 
round  which  it  must  revolve  easily.  When  the  rod  s  is  turned 
so  far  from  the  position  indicated  in  the  diagram,  that  the  little 
plates  t  are  no  longer  supported,  the  latter  will  turn  round, 
throwing  off  whatever  may  have  been  laid  upon  them.  It  is 
better  that  the  two  plates  t  should  not  turn  round  simultaneously. 
We  lay  then  a  piece  of  metal,  and  a  little  feather  on  each  plate; 
and  if  we  let  the  one  plate  turn  over  before  we  have  done  pump- 
ing, the  piece  of  metal  will  fall  much  faster  than  the  feather. 
But  when  the  air  is  quite  exhausted,  and  the  second  plate  is 
turned  over,  the  feather  will  fall  as  rapidly  as  the  piece  of  metal. 


CONDENSING   PUMP. 


139 


The  Condensing  Pump  serves  to  condense  the  air.     It  differs 
essentially   from    the    air 

pump,  in  having  valves  Fis-  117- 

that  open  and  shut  in  op- 
posite directions,  as  exhi- 
bited in  Fig.  117.  When 
the  piston  descends,  it 
compresses  the  air,  driving 
it  into  a  receiver ;  when  it 
ascends,  the  external  air 
opens  the  valve  of  the 
piston,  and  presses  into 
the  cylinder,  while  the  compressed  air  in  the  receiver  keeps  the 
bottom  valve  of  the  cylinder  shut.  Another  depression  of  the 
piston  re-opens  the  bottom  valve,  and  closes  the  piston  valve, 
when  a  new  supply  of  air  is  forced  into  the  receiver,  &c. 


Fig.  118. 


Fig.  119. 


140 


CONDENSING    PUMP. 


The  barometer  gauge  of  the  condensing  machine  is  a  straight 
tube,  closed  at  the  top  and  filled  with  air,  having  its  lower  open 
end  plunged  in  a  vessel  of  mercury.  On  beginning  the  experi- 
ment, the  air  into  the  tube  is  below  the  pressure  of  one  atmo- 
sphere, if  the  levels  of  the  mercury  in  the  tube  and  the  vessel  are 
of  equal  weight. 

The  more  the  pressure  increases,  the  higher  the  mercury  rises 
in  the  tube.  From  the  height  of  this  column  of  mercury,  and  the 
compression  of  the  air  in  the  tube,  it  is  easy  to  determine  the 
degree  of  condensation  in  the  receiver. 

In  this  machine,  the  receiver  must  be  screwed  tightly  on  the 
plate  to  prevent  its  being  raised  by  the  compressed  air. 

Condensing  pumps  have  been  so  contrived  as  to  screw  on  the 
apparatus  in  which  air  is  to  be  compressed.  They  have  only  one 
cylinder,  and  one  piston  without  a  valve.  On  the  one  end  of  the 
cylinder,  the  reservoir  is  screwed  on,  in  which  the  air  is  to  be 
compressed ;  on  this  there  is  a  valve,  through  which  air  may  enter, 
but  cannot  escape  from  the  reservoir.  In  order  to  admit  fresh  air 
into  the  cylinder,  after  a  portion  has  been  compressed  into  the 
reservoir,  the  cylinder  has  either  a  lateral  aperture  as  in  Fig.  118, 
or  a  lateral  valve  like  Fig.  119.  The  latter  is  particularly  appli- 
cable when  we  want  to  compress  a  special  gas,  for  it  is  then  only 
necessary  to  put  the  glass  reservoir  in  connection  with  the  tube  of 
the  lateral  valve. 

The  first  of  these  condensing  pumps  is  mainly  used  for  loading 
air  guns,  the  construction  of  which  will  be  made  clear  by  the 
accompanying  figures.  When  by  help  of  the  condensing  pump, 


Fig.  120 


HERO'S   BALL.— THE   FIRE   ENGINE.  141 

we  have  compressed  the  air  in  the  piston  of  the  air  gun  to  the 
density  of  8  or  10  atmospheres,  a  barrel  is  screwed  on,  along 
which  the  ball  is  directed.  If  the  valve  closing  the  piston  be 
opened  by  the  trigger,  a  part  of  the  enclosed  air  will  escape  with 
great  violence,  carrying  the  ball  with  it;  but  the  valve  closes 
immediately.  A  good  air  gun  may  give  as  much  speed  to  a  ball 
as  a  musket  can  do.  Many  shots  may  be  discharged  without 
reloading,  the  number  being  in  proportion  to  the  size  of  the 
piston. 

Hero's  Ball. — We  can  also  force  fluids  out  of  vessels  with  great 
violence  by  means  of  compressed  air,  as  is  the  case  with  Hero's 
Ball.  A  tube  passes  nearly  to  the  bottom,  through  the  neck  of 
a  vessel  partially  filled  with  water.  The  tube  termi- 
nates above  in  a  point  with  a  fine  aperture.  If  the 
air  in  the  upper  part  of  the  vessel  have  in  any  way 
been  compressed,  the  pressure  which  it  exerts  on 
the  surface  of  the  water  will  drive  the  fluid  out  of 
the  fine  aperture  after  the  manner  of  a  fountain. 
We  may  make  use  of  a  flask,  closed  by  a  cork, 
through  which  passes  a  glass  rod  drawn  out  to  a 
fine  point.  If  the  glass  rod  does  not  penetrate  far 
into  the  vessel,  we  obtain,  by  this  arrangement,  the 
dropping  bottle  with  which  chemists  commonly  wash 
their  precipitates.  The  air  in  this  may  be  com- 
pressed by  blowing  with  the  mouth  through  the  tube.  If  the 
air  enclosed  in  the  apparatus  be  of  equal  density  with  the  sur- 
rounding atmosphere,  and  we  place  it  under  the  bell  of  the  air 
pump,  it  will  begin  to  burst  as  soon  as  we  have  exhausted  the 
air.  This  apparatus  is  often  constructed  in  large  dimensions  en- 
tirely of  metal.  In  that  case,  the  neck  is  furnished  with  a  cock, 
above  which  the  thin  tube  may  be  screwed  on.  The  air  is 
compressed  by  means  of  a  condensing  pump  screwed  on  in  the 
place  of  the  pointed  tube.  When  the  vessel  is  charged,  we  close 
the  cock,  remove  the  pump,  and  screw  on  the  pointed  tube.  As 
soon  as  the  cock  is  opened,  the  water  rushes  out  to  the  height  of 
from  30  to  100  feet,  if  the  air  has  been  compressed  to  2,  or  from 
5  to  6  atmospheres. 

The  Fire  Engine. — Fig.  124  represents  the  combination  of  the 
forcing  pump  with  Hero's  Ball ;  the  cylinders,  of  which  we  will 
consider  the  one  to  the  right  hand,  stand  in  a  trough  filled  with 


142  HERO'S    FOUNTAIN. 

Fig.   124. 


water.  If  thepiston^/be  raised,  the  valve  d  rises,  and  the  water 
presses  into  the  cylinder  e.  On  the  descent  of  the  piston,  the  valve 
d  closes,  the  valve  c  is  opened,  and  the  water  is  forced  through  the 
narrow  tube  6,  into  the  air  chamber  a.  This  air  chamber  is  no- 
thing more  than  a  large  Hero's  Ball,  and  the  more  water  is  pumped 
into  it,  the  more  is  the  air  in  its  upper  part  compressed.  The 
tube  h  reaches  almost  to  the  bottom  of  the  air  chamber ;  at  g  a 
tube  with  a  narrow  opening  is  screwed  on.  A  strong  jet  of  water 
is  driven  from  the  aperture  by  the  pressure  constantly  exercised 
upon  the  water  by  the  air  compressed  in  the  chamber.  A  leather 
pipe,  with  a  metal  spout,  may  be  screwed  to  an  opening  in  the 
side  of  the  air  chamber  near  the  bottom  ;  this  pipe,  also,  throws 
out  a  jet  of  water  which  can  be  more  easily  directed,  and  brought 
nearer  to  the  burning  parts  than  the  stream  from  the  aperture  g. 
The  raising  and  lowering  of  the  piston  are  managed  by  a  lever, 
wThose  fulcrum  is  m.  Both  rods  of  the  pistons  are  so  attached  to 
this  lever,  that  the  one  ascends  as  the  other  descends,  and  a  fresh 
supply  of  water  may,  therefore,  be  uninterruptedly  conveyed  to 
the  air  chamber. 

Hero's  Fountain. — The  most  simple  mode  of  constructing  Hero's 
Fountain  by  means  of  glass  tubes,  and  a  glass-blower's  lamp  is 
shown  in  Fig.  125.  The  column  of  water  in  the  tube  a  com- 
presses the  air  in  6 ;  the  compressed  air  presses  upon  the  sur- 
face of  the  water  in  c,  and  consequently  the  water  must  gush  out 


MEASUREMENT    OF    THE    PRESSURE    OF    GASES. 


143 


at   d.      According  to   the    same         Fis- 125-  Fis-  126- 

principle,  Hero's  Fountain  in  Fig. 

126  is  composed  of  glass  tubes, 

glass  flasks,  and  a  funnel.     It  is 

evident  that  the  vessel  c  must  be 

supported  in  some  way.     When 

the  apparatus  is   set  into  action, 

the  vessel  c  is  filled  with  water, 

and  its  neck  closed  with  a  cork, 

through  which  pass  the  tubes  b 

and  d.     Water  is  then  poured  into 

the  funnel  /,  on  which  the  water 

begins  to  gush  from  the  tube  d. 

Measurement  of  the  Pressure  of 
Gases. — There  are  two  means  by 
which  we  may  measure  the  pres- 
sure of  gases,  viz.,  by  columns  of 
liquids,  and  by  valves.  An  appa- 
ratus designed  for  this  purpose  is 
termed  a  manometer.  The  baro- 
meter gauge  upon  the  air  pump, 
and  the  condensing  machine  are  manometers. 

Safety  tubes  belong,  in  some  respects,  to  mano- 
meters,  for  they  measure  the  pressure  of  the  gas  in 
the  apparatus  to  which  they  are  attached.  If  their 
tension  be  equal  to  the  atmospheric  pressure,  the 
fluid  will  stand  at  the  same  level  in  both  limbs, 
(Fig.  127;)  if  this  be  not  the  case,  the  pressure  may 
be  determined  in  the  interior  of  the  enclosed  space 
by  the  difference  of  the  columns  of  liquid  in  the  two 
limbs,  provided  the  density  of  the  liquid  in  the  safety 
tube  be  known.  These  safety  tubes  were  invented 
by  Welter,  and  are  of  the  greatest  utility  in  many 
chemical  operations,  by  preventing  explosions,  as 
well  as  the  forcing  back  of  enclosed  liquids  by  the 
air's  pressure  when  absorption  takes  place. 

In  Figs.  128  and  129  there  are  two  loaded  or  safety  valves  re- 
presented. If  the  weight  be  known  that  will  load  such  a  valve, 
and  the  size  of  the  surface  of  the  valve  which  has  to  support  the 
vertical  pressure  of  the  gas,  the  tension  of  the  gas  at  the  moment 


Fig.  127. 


144 


MEASUREMENT    OF    THE    PRESSURE    OF    GASES. 


129- 


when  it  is  able  to 
raise  the  valve  may 
be  calculated.  For 
instance,  if  the  load- 
ing of  the  valve  be 
100  kilog.,  and  the 
area  of  the  value  25 

square  centimetres,  each  square  centimetre  of  this  area  will  have 
to  bear  4  kilogrammes.  As  now  the  pressure  of  the  atmosphere 
upon  each  square  centimetre  amounts  to  1,0325,  the  tension  of 

the  gas  able  to  lift  this  valve  will  be  equal  to  -  -  =3,87at- 

1,0325 

mospheres,  to  which  must  be  added  one  atmosphere  more,  on  ac- 
count of  the  pressure  of  the  air,  borne  by  the  valve  besides  its 
other  load.  This  apparatus  is  applied  to  liquids  as  well  as  gases, 
and  by  its  means,  the  boilers,  tubes  of  communication,  and  the 
cylinders  of  the  steam  engine  are  proved. 


ATTRACTION    BETWEEN    SOLID    BODIES.  145 


CHAPTER  VI. 

ATTRACTION  BETWEEN  GASEOUS  AND  SOLID,  AS  WELL  AS  BETWEEN 
GASEOUS  AND  LIQUID  BODIES. 

THE  following  experiments  prove  most  evidently  that  a  con- 
siderable attraction  exists  between  the  particles  of  solid  and  gaseous 
bodies.  If  we  place  a  piece  of  glowing  char-  Fi  130 

coal  under  mercury,  and  then  let  it  ascend 
into  a  cylinder,  whose  upper  part  is  filled  with 
carbonic  acid,  shut  off  by  means  of  the  mer- 
cury from  any  communication  with  the  exter- 
nal air,  and  whose  volume  is  about  20  times 
greater  than  that  of  the  charcoal,  the  carbonic 
acid  will  in  a  few  minutes  be  so  condensed  by 
the  charcoal,  that  the  mercury  will  rise  to  the 
top  of  the  cylinder.  The  whole  mass  of  the 
carbonic  acid,  which  before  filled  all  the  upper  part  of  the  cylinder, 
is  now  condensed  by  the  attraction  existing  between  the  gas  and 
the  pores  of  the  charcoal,  the  former  having  been  absorbed.  A 
similar  experiment  succeeds  with  many  other  gases.  If  the  char- 
coal have  lain  any  length  of  time  in  the  air,  the  experiment  does 
not  prove  quite  successful,  as  we  may  easily  understand,  if  we 
reflect  that  it  absorbs  atmospheric  air  and  the  vapor  distributed 
through  the  air,  and  that  its  capacity  for  absorbing  other  gases  is 
consequently  diminished. 

If  charcoal  that  has  absorbed  gas  be  brought  under  the  air- 
pump,  or  kindled,  it  will  liberate  the  absorbed  gas. 

Absorption  of  gases  is  at  all  times  accompanied  by  a  develop- 
ment of  heat,  which  is  more  considerable  in  proportion  to  the 
amount  of  absorption. 

In  the  manufacture  of  gunpowder,  the  charcoal  is  triturated  to 
a  very  fine  powder,  which  absorbs  atmospheric  air  with  such 
13 


146  ATTRACTION    BETWEEN    SOLID    BODIES. 

avidity  that  a  considerable  degree  of  heat  takes  place  in  the  mass, 
and  frequently  gives  rise  to  combustion. 

If  a  fine  jet  of  hydrogen  gas  be  thrown  upon  spongy  platinum, 
absorption  of  the  gas  follows  with  such  violence  as  to  make  the 
platinum  red  hot,  and  inflame  the  hydrogen  gas.  On  this  prin- 
ciple Dobereiner's  lamp  is  constructed. 

Absorption  is  considerably  promoted  when  the  solid  body  is  in 
a  finely  divided  condition,  as  is  the  case  with  charcoal  powder 
and  spongy  platinum,  because  of  the  increased  number  of  points 
of  contact  between  the  solid  bodies  and  the  gas,  but  this  finely 
porous  condition  is  not  indispensable  to  effect  a  condensation  of 
the  gas  ;  it  also  occurs  if  the  solid  body  has  a  perfectly  smooth,  or 
metallic  surface  ;  in  this  case,  however,  the  condensation  is  less 
considerable.  If  we  put  a  piece  of  platinum,  having  a  perfectly 
smooth  metallic  surface,  into  a  mixture  of  oxygen  and  hydrogen, 
both  gases  will  be  so  much  condensed  as  gradually  to  combine 
and  form  water. 

Not  only  platinum  and  charcoal,  but  all  solid  bodies,  exhibit  in 
a  greater  or  less  degree  this  remarkable  relation  to  gases.  Every 
solid  body  is  as  it  were  surrounded  by  the  condensed  atmosphere 
of  some  gas,  which  it  is  often  very  difficult  to  separate  from  it,  and 
which,  even  if  its  surface  be  perfectly  freed  from  it,  will  again 
adhere  after  a  time,  if  the  body  come  into  contact  with  gases. 
Thus,  for  example,  glass  is  always  surrounded  by  a  coating  of 
condensed  air,  which,  in  the  construction  of  barometers,  can  only 
be  removed  by  the  boiling  of  the  mercury  in  the  tube.  If  water 
be  poured  into  a  glass  flask,  and  placed  over  the  fire,  there  is 
soon  seen  a  number  of  bubbles  forming  on  the  bottom  long  before 
the  water  boils.  This  is  owing  to  the  layer  of  air,  which,  from 
its  great  condensation,  was  before  imperceptible,  but  now  forms 
bubbles  after  its  expansion  by  heat.  Similar  bubbles  appear  if 
the  vessel  with  water  be  placed  under  the  receiver  of  the  air-pump, 
and  then  exhausted. 

Such  gaseous  bodies  as  easily  pass  over  into  a  fluid  condition 
(vapor)  are  rendered  liquid  by  their  attraction  for  solid  bodies. 
Thus  chloride  of  calcium  attracts  the  vapor  of  water  with  great 
rapidity,  condenses  it  to  water,  and  at  length  dissolves  in  the  water. 
Common  salt  also  attracts  the  vapor  of  water  from  the  air,  and 
becomes  moist.  It  is  the  same  with  potash  and  many  other 
bodies. 


ABSORPTION    OF    GASES    BY    LIQUIDS.  147 

Bodies  that  attract  the  vapor  of  water  from  the  air  are  called 
hydroscopic  bodies ;  to  these  belong,  besides  those  we  have  men- 
tioned, wood,  hair,  whalebone,  &c. 

Absorption  of  gases  by  liquids. — Liquids  exhibit  a  similar  rela- 
tion to  gases  as  that  we  have  just  considered  in  solid  bodies.  This 
may  be  made  evident  by  so  far  altering  the  experiment  given  in 
Fig.  130,  as  to  substitute  ammoniacal  gas  for  carbonic  acid,  and 
water  for  charcoal.  The  ammoniacal  gas  is  so  eagerly  absorbed 
by  the  water,  that  all  the  gas  disappears  at  once,  and  the  tube 
becomes  filled  with  water. 

The  water  absorbs  700  times  its  volume  of  ammoniacal  gas,  and 
500  times  its  volume  of  muriatic  acid  gas.  The  power  of  absorp- 
tion of  liquids  depends  upon  the  temperature  and  degree  of  pres- 
sure. Liquids  absorb  larger  quantities  of  gas  at  a  low  tempera- 
ture, and  under  strong  pressure,  than  a  high  temperature,  and 
under  less  pressure. 

Water  almost  always  contains  a  tolerably  large  quantity  of 
absorbed  air,  from  which  it  can  only  be  freed  by  prolonged 
boiling.  Carbonic  acid,  amongst  other  gases,  is  pretty  freely 
absorbed  by  water,  as,  for  instance,  beer,  champagne,  and  certain 
mineral  waters. 


148  REST    AND   MOTION. 


SECTION    III. 

OF  MOTION  AND  ACCELERATING  FORCES. 


CHAPTER    I. 


DIFFERENT  KINDS  OF  MOTION. 


Rest  and  Motion. — A  body  that  changes  its  position  with  respect 
to  another  is  in  motion;  it  is  at  rest  if  no  such  change  occur. 
Every  form  of  rest  or  motion  observed  by  us  is  only  relative, 
absolute.     The  trees  are  at  rest  in  relation  to  the  neighboring 
hills ;  trees  have  an  unchangeable  position  on  the  earth's  surface 
but  trees  and  hills  are  not  on  that  account  in  a  state  of  absolute 
rest ;  they  with  the  whole  earth  on  which  they  stand  traverse  the 
vast  orbit  of  our  planet.     Although  we  know  that  we  fly  throu^ 
the  space  of  heaven  with  the  earth,  as  it  revolves  round  the  sui 
we  cannot  say  anything  definite  respecting  our  own  absolute 
motion,  as  we  know  not  whether  the  sun  is  an  immovable  centi 
of  the  world.     Everything,  however,  seems  to  imply  that  the  sui 
itself  is  only  a  planet  revolving  round  another  sun,  which  in  it 
turn  is  not  fixed;  but  we  are  not  able  to  determine  or  even 
conjecture  what  the  centre  of  all  motion  is. 

There  are  two  essential  points  regarding  motion  that  we  mus 
consider,  viz.,  direction  and  velocity.  If  a  body  move  continually 
in  one  direction,  its  course  is  in  a  straight  line ;  but  if  the  direc 
tion  of  its  motion  constantly  change,  its  motion  is  curvilinear. 
If  we  draw  a  tangent  to  the  curve  at  a  point  of  the  curve  occu- 
pied by  the  body  at  any  given  instant,  this  tangent  will  show  the 
direction  of  the  motion  of  the  body  at  that  moment. 

Uniform  motion. — A  body  has   a  uniform  motion  if  it  pas 
over  equal  spaces  in  equal  times.    If  a  body  moving  in  a  straight 


UNIFORM  MOTION.  149 

line,  advance  equally  far,  sixty  feet  for  instance,  in  each  minute, 
thirty  feet  in  every  half  minute,  and  one  foot  in  every  second,  it 
moves  uniformly.  As  the  spaces  traversed  in  equal  times  are 
equal,  it  follows  that  the  relation  between  time  and  space  remains 
constant.  This  relation  we  term  the  velocity  of  uniform  motion. 
If  we  take  double  or  triple  the  time,  the  space  traversed  will  be 
doubled  and  tripled ;  and  the  relation  consequently  remains  the 
same.  The  number  expressing  the  velocity  depends  upon  the 
units  chosen  for  space  and  time.  If  we  were  only  to  express  the 
velocity  by  a  number,  without  giving  the  units  employed,  the 
velocity  would  then  be  wholly  undefined.  The  simplest  mode  of 
expressing  velocity  is  by  giving  the  space  traversed  by  the  body 
in  a  unit  of  time,  as  a  minute  or  a  second.  Thus,  for  instance, 
a  man  walks,  as  a  general  rule,  with  the  velocity  of  2.5  feet  in  a 
second.  An  ordinary  wind  has  a  velocity  of  3.28  feet  in  the 
second;  a  hurricane  118.08  in  a  second. 

[The  following  table  from  the  Ann.  de  Bureau  des  Longitudes, 
1828,  gives  the  rapidity  of  the  motion  of  the  air  per  second  in 
different  winds. 

1.64  feet        .         .         .     Scarcely  perceptible  wind. 
3.28    "...     Sensible  breeze. 
6.56    "...     Moderate  wind. 

18.04   "...     Brisk  " 

32.80   "          .         .         .     Strong         " 

65.60   "...     Violent         " 

73.80   "...     Tempest. 

88.56    "...     Violent  tempest. 
118.08  "...     Hurricane. 
147.60  "...     Violent  hurricane.] 
These  two  last  named  velocities  admit  of  comparison,  as  they 
are  expressed  in  the  same  units ;  thus  the  velocity  of  the  hurri- 
cane is  45  times  as  great  as  that  of  an  ordinary  wind.     If  we 
would  compare  the  speed  of  a  man  with  the  velocity  of  an  hurri- 
cane, we  must  first  reduce  both  to  a  like  unit.   As  matter  is  inert, 
a  body  once  having  a  uniform  motion  would  continue  to  move 
in  the  same  direction,  and  with  the  same  velocity,  unless  a  second 
force  were  to  act  upon  it,  changing  its  direction  alone,  or  its  velo- 
city alone,  or  both ;  for  by  itself  a  body  can  change  nothing  in 
this  respect,  either  with  regard  to  its  conditions  of  rest  or  motion. 
Thus  we  are  to  understand  the  law  of  inertia,  and  not  as  the 

13* 


150  ACCELERATED   AND    RETARDED    MOTION. 

older  philosophers,  who  maintained,  that  matter  had  a  prevailing 
tendency  to  rest.  If  we  see  that  the  motion  of  a  body  be  in  any 
way  changed,  if,  for  instance,  its  velocity  increases  or  diminishes, 
its  motion  ceases,  or  changes  its  direction,  then  must  this  change 
always  be  occasioned  by  some  external  cause.  A  stone  thrown 
towards  the  sun  would  continue  its  course  till  it  reached  the  sun, 
were  it  not  prevented  by  the  resistance  of  the  air,  and  by  the  force 
of  gravity  drawing  it  back  to  the  earth. 

Accelerated  and  retarded  motion. — A  constant  change  of  velo- 
city can  only  be  effected  by  a  constantly  acting  force,  termed 
accelerating  or  retarding,  according  as  it  augments  or  diminishes 
motion.  If  at  any  moment  of  the  varying  motion,  all  the  accele- 
rating or  retarding  forces  were  to  cease  to  act,  the  motion  would 
become  uniform  from  that  moment.  The  velocity  of  a  varying 
motion  in  a  given  moment  is  determined  by  computing  how  far 
the  body  would  move  in  the  unit  of  time,  if  all  acceleration  and 
retardation  were  to  cease  from  the  said  moment. 

A  motion  is  termed  uniformly  accelerated,  or  uniformly  retarded 
if  the  velocity  increase  or  diminish  equally  in  equal  times.  Such 
motions  are  produced  by  forces  acting  continually  with  the  same 
intensity  as  is  the  case  with  gravity.  A  heavy  body  falls  with  an 
uniformly  accelerated  velocity.  If  we  set  out  with  the  supposi- 
tion that  the  intensity  of  gravity  is  the  same  at  the  different  places 
traversed  by  the  falling  body,  (and  experience  justifies  us  in  this 
assumption  at  least  within  certain  limitations,)  all  laws  of  freely 
falling  bodies  may  be  developed  by  a  simple  mode  of  reasoning. 

As  gravity  acts  in  the  same  manner  at  every  moment  of  a  fall, 
the  velocity  of  the  falling  body  must  also  increase  equally,  on 
equal  terms,  that  is,  the  motion  must  be  a  uniformly  accelerated 
one.  If  the  falling  body  attain,  in  the  first  second  of  its  descent, 
a  velocity  g,  it  must  after  2,  3,  4  ...  t  seconds  have  attained  to 
a  velocity  of  2g,  3g,  4g  .  . .  t .  g-,  which  may  be  thus  generally 
expressed  in  words :  the  velocity  of  a  freely  falling  body  is  always 
proportionate  to  the  time  elapsed  during  its  fall:  or  it  is 

v=g.t 

if  v  represent  the  velocity  acquired  by  the  body  during  its  fall  in 
t  seconds,  and  g  its  velocity  at  the  end  of  the  first  second. 

What  space  will,  therefore,  the  body  fall  through  in  1,  2,  3,  4 
....  £  seconds?  At  the  beginning  of  the  first  second,  its  velocity 
is  equal  to  o;  at  the  end  of  the  same,  it  is  g.  As  now  the 


ACCELERATED    AND    RETARDED   MOTION.  151 

velocity  increases  uniformly,  the  space  fallen  through  in  one  second 
must  clearly  be  the  same  as  if  the  body  were  during  one  second 
moved  by  a  velocity  ranging  half  way  between  the  beginning  and 
ending  velocity  ;  that  is  between  o  and  g.  But  this  medium 
velocity  is  ^g,  and  a  body  falling  during  one  second  with  a  velocity 
of  J  g,  passes  over  a  space  J  g. 

In  the  same  manner,  we  may  find  by  deduction,  the  space  passed 
through  by  a  body  falling  during  two  seconds.  The  starting  velo- 
city is  o  ;  the  closing  velocity  2g;  the  medium  velocity  is  conse- 

quently —  i.  and  a  body  moving  during  two  seconds  with  this 
velocity,  passes  through  a  space  equal  to  2.2?  . 

In  three  seconds  the  body  passes  through  a  space  equal  to  3.3  ?  9 
for  the  starting  velocity  is  0,  the  closing  velocity  3  g,  and  the 

medium  velocity  is  consequently  equal  to  3  ?.  ;  and  a  body  must 

& 

move  uniformly  with  this  velocity  during  three  seconds,  if  it  tra- 
verse the  same  space  through  which  a  heavy  body  will  fall  in  the 
same  time.  We  will  express  this  generally:  If  a  body  fall  during 
t  seconds,  it  must  traverse  a  space  equal  to  what  it  would  have 
done  during  the  same  time  with  a  uniform  motion,  if  its  velocity 

cr 

were  a  medium  between  o  and  g  .  t,  that  is  ^  .  t.  But  a  body  mov- 

er 
ing  t  seconds  with   a  velocity  equal  to  5  t  traverses  a  space 


or,  expressed  verbally  :  the  spaces  described  are  proportional  to  the 
squares  of  the  times. 

Experiment,  however,  can  alone  prove  whether  these  premises 
be  correct,  and  whether  gravity  actually  be  a  uniformly  accele- 
rating force.  This  question  cannot  be  directly  solved,  since  the 
velocity  with  which  bodies  fall,  augments  so  rapidly,  that  after  the 
first  few  moments  it  becomes  impossible  to  determine  accurately 
the  spaces  passed  through  in  given  times.  But  although  we 
cannot  find  this  by  direct  experiment,  we  may  arrive  at  the  result 
by  indirect  means.  The  most  simple  method  is  Galileo"*  s  inclined 


152  GALILEO'S    INCLINED    PLANE. 

plane;  but  the  one  possessed  of  the  greatest  degree  of  accuracy  is 
Jitwooffs  falling  machine. 

Galileo's  Inclined  Plane.— -Galileo  studied  the  laws  of  descent 
by  rolling  easily  moving  bodies  down  an  inclined  plane.     To  fol- 
low his  experiments,  it  is  best  to  make  use  of  a  canal  of  wood,  about 
10  or  12  feet  in  length  (Fig.  131),  polished  as  smoothly  as  pos- 
Fig.  131.  sible  in  the  interior,  and 

divided  into  feet  and 
inches.  The  canal  must 
be  inclined  by  being 
supported  at  one  end.  If 
it  were  placed  perfectly  horizontally,  a  ball  laid  upon  it  would  re- 
main at  rest,  owing  to  its  gravity  being  entirely  counterpoised  by 
the  resistance  of  its  horizontal  support.  If  the  canal  were  placed 
vertically,  the  ball  would  fall  freely  with  the  whole  force  of  its 
gravity;  but  if  the  body  be  inclined,  the  force  of  gravity  will  be 
diminished  in  a  certain  fixed  relation.  It  follows  from  the  prin- 
ciples of  statics,  that  we  obtain  the  amount  of  accelerating  force 
urging  the  ball  down  the  inclined  plane,  if  we  multiply  the 
accelerating  force  of  gravity  with  the  sine  of  the  angle  of  inclina- 
tion of  the  plane.  Whatever  may  be  the  relation  in  which  a  force 
is  diminished,  whether  it  be  reduced  to  the  half,  the  third,  or  the 
fourth  part  of  its  original  amount,  the  absolute  amount  of  the  mo- 
tion produced  will  alone  be  changed,  while  the  relations  of  the 
spaces  traversed  in  given  times  will  remain  the  same.  The  laws 
derived  from  experiments  with  the  inclined  plane,  are  therefore 
the  true  laws  of  gravity.  If  we  slip  a  ball  at  a  definite  moment 
from  the  upper  end  of  the  canal,  and  note  the  spaces  traversed  in 
1,  2,  3,  seconds,  we  shall  find  that  the  spaces  are  as  the  squares 
of  the  time  necessary  to  traverse  those  spaces.  Gravity  is,  there- 
fore, really  a  uniformly  accelerating  force. 

Jltwootfs  Falling  Machine  consists  essentially  of  a  pulley 
revolving  round  a  horizontal  axis,  and  fastened  to  the  top  of  a 
vertical  column,  about  7  feet  in  height  (Fig.  132).  A  string  is 
slung  over  the  pulley  having  equal  weights  m  at  its  extremities. 
If  we  attach  an  extra  weight  n  on  the  one  side,  equilibrium  will 
be  disturbed;  the  weights  m  and  n  will  sink  on  one  side,  and  the 
weight  m  on  the  other  \vill  be  raised  up.  The  velocity  with 
which  this  takes  place  is  much  less  considerable  than  in  a  free 


ATWOOD'S    FALLING   MACHINE. 


153 


Fig.  132. 


fall,  because  the  moving  force,  the  force  of  gravity  of  the  extra 
weight  n,  has  not  only  to  set  in  mo- 
tion the  mass  m,  but  also  the  mass 
2  m  +  n. 

If,  for  example,  each  of  the  weights 
m  were  7  oz.,  but  n  1  oz.  only,  the 
extra  weight  of  1  oz.  would  have  to 
put  a  mass  of  15  oz.  in  motion;  the 
motion  will  follow  the  same  laws,  as 
in  a  free  fall,  with  this  difference 
only,  that  the  intensity  of  the  accele- 
rating force  is  here  15  times  smaller. 
If,  therefore,  a  freely  falling  body 
traverse  15  feet  of  space  during  the 
first  second,  the  space  traversed  in 
this  case,  in  the  first  second,  will  be 
only  1  foot. 

It  is  easy  to  see  that  the  motion 
will  be  slower,  the  smaller  the  extra 
weight  n  is  in  relation  to  mj  and  we 
may,  therefore,  by  proper  alterations 
in  Uj  make  the  motion  as  slow  as  we 
choose. 

The  vertical  column  has  been  di- 
vided into  feet,  for  the  greater  con- 
venience of  measuring  the  spaces  of 

falling.  The  upper  point  is  the  zero  of  the  scale.  Two  slides, 
one  of  which  is  perforated,  can  be  secured  to  any  part  of  the 
scale. 

It  is  necessary  to  know  thus  much  of  the  apparatus  in  order  to 
understand  the  experiments.  In  the  first  place,  it  is  easy  to  prove, 
by  means  of  this  machine,  that  the  space  is  as  the  square  of  the 
time  of  falling.  Let  n  be  so  chosen  that  the  descent  in  the  first 
second  is  1  inch.  If  the  lower  end  of  the  weight  m,  carrying  the 
extra  weight,  be  at  the  zero  point  of  the  scale,  the  weight  will  be 
at  the  first  mark  below  zero,  in  the  course  of  one  second  from  the 
time  of  the  commencement  of  motion. 

If  the  space  traversed  during  the  first  second  of  falling  be  1 
inch,  it  must  be  4  inches  during  the  two  first  seconds ;  if,  there- 
fore, we  move  the  slide  to  4  inches  below  zero,  the  weight  that 


154  ATWOOD'S    FALLING   MACHINE. 

began  its  motion  at  the  point  zero,  will  strike  at  the  end  of  two 
seconds. 

If  we  let  the  motion  always  begin  from  the  same  point  of  the 
scale,  viz.,  from  zero,  the  slide  must  be  fixed  at  9, 16,  25,  36,  49, 
64  inches  below  that  point,  if  the  weight  is  to  strike  in  3,  4,  5,  6, 
7,  8  seconds.  This  experiment  fully  confirms  the  law,  that  the 
spaces  traversed  in  falling  are  as  the  squares  of  the  time  of 
falling. 

We  have  shown  above,  that  this  law  follows  from  the  assump- 
tion that  the  velocity  is  proportionate  to  the  time  of  falling.  The 
truth  of  the  inference  proves  also  indirectly  the  correctness  of  the 
assumption.  The  relation  existing  between  the  time  of  falling 
and  the  velocity  of  the  body  at  any  given  moment,  cannot  be 
directly  ascertained  either  in  a  free  descent,  or  by  means  of  the 
inclined  plane,  since,  in  order  to  obtain  this  result,  it  would  be 
necessary  that  the  velocity  of  the  body  should  not  increase  from 
that  moment ;  consequently  we  must  be  able  suddenly  to  destroy 
the  action  of  gravity  on  the  body.  By  means  of  the  falling- 
machine,  we  may  arrest  the  accelerating  force  at  any  moment. 
The  accelerating  force  is  only  the  gravity  of  the  extra  weight  n ; 
if,  now,  we  give  to  the  excess  of  weight  n,  the  form  represented  at 
Fi  133  ^S'  1^>  we  may  arres*  ft  by  means  of  the  perforated 
• — rm — .  slide  at  any  moment,  while  the  mass  m  continues  to 
'Ka)^1  progress  with  uniform  velocity  from  the  time  it  ceased  to 
be  acted  upon  by  an  accelerating  force.  We  may,  therefore,  by 
help  of  this  contrivance,  determine  directly  the  velocity  at  any  one 
moment  by  the  space  traversed  in  the  next  second. 

We  have  seen  that  if  g  be  the  velocity  of  the  body  at  the  end  of 
the  first  second  of  falling,  the  space  traversed  in  the  same  period 
of  time  will  be  ^  g.  If,  now,  we  have  so  arranged,  that  1  inch  is 
traversed  in  the  first  second,  the  closing  velocity  of  the  first  second 
will  be  2  inches ;  that  is,  if  at  the  close  of  the  first  second  the 
accelerating  force  cease  to  act,  the  body  will  traverse  in  the  next 
second  a  space  of  2  inches  with  uniform  velocity. 

It  is  easy  to  demonstrate  that  this  relation  actually  exists  be- 
tween the  time  and  velocity  of  falling.  Let  us,  for  instance,  so 
place  the  weights  m  +  n  before  motion  begins,  that  the  under 
surface  of  n  may  stand  at  zero  upon  the  scale ;  the  perforated  slide 
must  also  be  so  arranged  that  its  upper  surface  stand  at  1  inch, 
and  the  lower  slide  so  that  its  upper  surface  may  be  as  much 


ATWOOD'S    FALLING   MACHINE.  155 

below  the  mark,  3  inches,  as  the  height  of  the  weight  m  requires. 
If,  now,  we  start  the  weights  at  a  definite  moment,  the  extra 
weight  will  strike  in  1  second,  and  the  weight  m  in  2  seconds. 
The  upper  point  of  the  weight  m  has,  therefore,  traversed  the 
space  from  zero  to  1  with  accelerated  velocity  in  the  first  second, 
and  has  passed  in  the  next  second  from  1  to  3  with  a  uniform 
degree  of  velocity. 

That  the  velocity  is  really  uniform  after  the  removal  of  the  extra 
weight,  we  see  from  this,  that  if,  without  altering  anything  else,  we 
lower  the  slide  2,  4,  6,  8,  or  10  inches,  the  contact  occurs  1,  2, 
3,  4  or  5  seconds  later;  consequently  that  a  space  of  2  inches  is 

t   traversed  in  every  succeeding  second. 

If  we  had  so  arranged  the  extra  weight  n  that  2,  3,  4,  5,  &c., 

I  inches  were  traversed  in  the  first  second,  a  space  of  4,  6,  8,  10, 

I  &c.,  inches  would  be  passed  over,  provided  we  removed  the  extra 

[  weight  at  the  end  of  the  first  second. 

We  have  assumed  above  that  if  the  velocity  be  g  at  the  end  of 
the  first  second,  the  closing  velocity  in  2,  3,  4  seconds  will  be  2  g, 

3  #?  4  g.     Experiment  fully  confirms  this.     If  we  again  assume 
that  the  extra  weight  n  be  so  arranged,  that  in  the  first  second  1 
inch  will  be  traversed,  and  consequently  in  the  next  two  seconds, 

4  inches,  there  will  be  a  space  of  4  inches  passed  over  in  each 
succeeding  second,  provided  we  take  off  the  extra  weight  at  the 
close  of  two  seconds ;  if  we  did  not  take  off  the  extra  weight  before 
the  close  of  the  3d  and  4th  second,  that  is,  when  a  space  of  9  or 
16  inches  had  been  passed  over,  the  motion  would  continue  from 
that  time  with  a  uniform  velocity  of  6  or  8  inches. 

In  a  free  fall  the  value  of  g  may  be  taken  at  somewhat  more 
than  30  feet.  When  we  come  to  speak  of  the  pendulum,  we  will 
ive  a  more  accurate  estimate  of  its  value.  In  a  free  fall,  there- 
fore, according  to  the  above  proved  laws,  the  space  passed  over 
in  the  first  second  of  falling  must  be  about  15  Paris  feet,*  while 
in  2,  3,  or  4  seconds,  it  must  amount  to  60,  135,  240,  &c. 

Galileo  himself  made  experiments  regarding  the  free  descent 
of  bodies,  which  were  subsequently  repeated  by  Riccioli  and 
Grimaldi  from  the  Tower  Degli  Asinelli  in  Bologna;  Dechalles 
has,  however,  made  the  most  accurate  experiments  on  the  subject. 
The  observed  spaces  through  which  bodies  fall  are  always  smaller 

*  A  Paris  foot  is  1.066  ft.  English. 


156  ATWOOD'S    FALLING    MACHINE. 

than  we  might  be  led  to  expect  from  theory.  This  difference 
depends,  however,  solely  upon  the  resistance  of  the  air,  which 
increases  as  the  square  of  the  velocity.  In  the  falling  machine, 
and  the  falling-canal,  the  resistance  of  the  air  does  not  influence 
the  results. 

It  is  frequently  important  to  be  able  to  compute  directly  the 
velocity  corresponding  to  given  heights  of  descent.  A  formula, 
according  to  which  this  calculation  may  be  made,  is  obtained  from 

the  following  equations  :  v=g,t  and  s  =  €  t2.  By  the  elimina- 
tion of  t  we  find  that 


The  velocities  are,  therefore,  as  the  square  roots  of  the  spaces. 
If,  for  instance,  a  body  had  fallen  from  a  height  of  100  feet,  its 
velocity  would  be,  according  to  this  formula,  as  follows:  v  = 
v/2.30.ioo  =  77,4  .  .  feet  (without  taking  into  account  the  resist- 
ance of  the  air). 

When  a  body  is  projected  by  any  force  vertically  upwards,  it 
ascends  with  decreasing  velocity  ;  after  a  time  its  upward  motion 
ceases,  and  it  then  begins  to  fall.  The  laws  of  this  motion  follow 
immediately  from  the  foregoing.  Suppose  a  body  to  be  thrown 
upward  with  a  velocity  of  150  feet,  it  would  ascend  150  feet  in 
every  second,  provided  gravity  exercised  no  influence  upon  it. 
But  as  gravity  imparts  to  a  falling  body  in  1,2,  3,  4,  5  seconds,  a 
velocity  of  30,  60,  90,  120,  150  feet,  opposed  to  the  direction  of 
the  upward  motion,  it  is  evident  that  the  velocity  of  the  ascending 
body  is  at  the  end  of  the  1st  second  150  —  30  =  120  feet  ;  at  the 
close  of  2  seconds  this  velocity  is  150  —  60  =  90  feet  ;  at  the  close 
of  3  seconds  150  —  90  =  60  feet  ;  in  4  seconds  150  —  120  =  30 
feet;  and  finally  at  the  end  of  the  5th  second  150—150  =  0; 
and  now  consequently  the  body  begins  to  fall.  We  have  here  an 
illustration  of  a  uniformly  retarded  motion,  for  the  velocity  of  the 
ascending  body  diminishes  about  the  same  in  every  second,  viz., 
about  30  feet. 

Let  us  put  this  in  general  terms.  If  n  be  the  velocity  at  the 
beginning  of  the  ascent,  the  velocity  of  the  body  will  after  t 
seconds  be 

v  =  n  —  g't. 

The  body  ceases  to  ascend,  when  n  =  g  t,  that  is,  when  the 


ATWOOD'S   FALLING   MACHINE.  157 

velocity  acquired  in  falling  during  t  seconds  is  equal  to  the  velo- 
city with  which  the  body  began  to  ascend. 

The  time  required  by  the  body  to  reach  the  highest  point  of  its 
course,  is 

f-5. 
8 

Let  us  now  endeavor  to  ascertain  the  height  attained  by  an 
ascending  body  in  a  given  time.  According  to  the  above  given 
illustration,  the  body  would  have  attained  a  height  of  150,  300, 
450,  &c.,  feet,  in  1,  2,  3,  &c.,  seconds,  provided  gravity  had  not 
drawn  it  down.  But  as  we  have  seen,  gravity  draws  it  down  15 
feet  in  1  second;  4  .  15  =  60  feet  in  2  seconds;  and  9  .  15  = 
135  feet  in  3  seconds.  The  height  at  the  end  of  1  second  is, 
therefore,  150 —  15  =  135  feet;  at  the  end  of  2  and  3  seconds, 
300  —  60  =  240  feet,  and  450  —  135  =  315  feet.  In  5  seconds 
it  would  have  reached  a  height  of  750  feet,  but  being  drawn  down 
15  X  52  =  375  feet  by  the  force  of  gravity,  it  is  actually  at  an 
elevation  of  750  —  375  =  375  feet,  and  now  begins  again  to  fall. 

Let  us  consider  this  more  generally.  In  t  seconds  the  body 
would  ascend  to  the  height  n  t,  owing  to  its  original  velocity  n ; 

but  having  been  drawn  down  ^  t2  by  gravity,  its  actual  height  is 
h  =  nt2  —  f  t2. 

A 

The  body  ascends  as  long  as  n  t  is  greater  than  ?  t2. 

As  the  highest  point  of  its  course  is  attained  when  t  =  -,  we 

g 
find  the  elevation  of  the  body  at  this  moment,  if  in  the  above 

given  formula  for  h,  we  substitute  this  value  in  place  of  £;  we 
then  have 

T n2       g  n2    _n2       n2        n2 

~g  ~2g~*~g  '~2g~2g' 
But  in  -  seconds  a  body,  falling  free,  traverses  a  space 

o 

g     n2 n2 

2  •  ?  ~  %' 

Hence  it  follows  that  the  body  requires  exactly  as  much  time 
to  fall  as  to  rise. 
14 


158 


PROJECTILES.— CENTRAL    MOTION. 


Let  us  seek  the  velocity  with  which  the  falling  body  regains 
the  point  from  whence  it  began  its  ascending  motion.  We  shall 

find  it  from  the  formula  v  =  g  tj  but  as  the  time  of  falling  t  =  - 

o 

it  follows  that  v  —  n9  that  is,  the  body  comes  down  with  the  same 
velocity  with  which  it  began  to  rise;  or,  in  order  to  impel  a  body 
vertically  to  a  height  h,  we  must  impart  to  it  an  initial  velocity 
exactly  as  great  as  that  acquired  by  it,  in  its  free  fall  from  the 
height  h. 

Projectiles. — If  a  body  be  thrown  in  any  other  than  a  vertical 
direction,  it  will  describe  a  curved  line,  the  form  of  which  may  be 
easily  deduced  from  the  laws  of  falling. 
Let  us  assume  the  simplest  case,  for 
instance,  that  the  body  be  impelled  by 
any  force  in  a  horizontal  direction.  If 
there  were  no  such  force  as  gravity,  the 
body  would  continually  move  in  a  hori- 
zontal direction,  and  with  an  uniform 
velocity. 

By  reason  of  the  first  impelling  force, 
it  would  traverse  the  space  a  b  in  1 
second,  the  equally  large  space  b  c  in  2 
seconds,  and  so  on,  and  must  conse- 
quently, at  the  end  of  the  1st,  2d,  3d, 
&c.,  second,  have  reached  the  points  6, 
c,  d,  &c.  But  it  has  sunk  from  the  force 
of  gravity;  in  the  first  second  it  fell  15  feet,  consequently  at  the 
end  of  that  time  instead  of  being  at  6,  it  will  be  15  feet  below  it. 
At  the  end  of  the  next  second,  it  is  60  feet  below  c;  at  the  end  of 
the  third,  135  feet  below  d,  &c.  The  curved  line  described  by 
the  body,  in  this  manner,  is  a  parabola. 

If  an  impulse  be  given  in  any  other  direction,  the  course  de- 
scribed may  in  like  manner  be  obtained  by  construction. 

The  course  described  by  a  projected  body  varies,  in  consequence 
of  the  resistance  of  the  air,  from  a  true  parabola. 

Central  Motion. — We  must  now  consider  motions  produced  by 
gravity,  where  the  directions  of  the  force  of  gravitation  in  various 
points  of  the  course  are  no  longer  parallel.  Motions  such  as  these 
are  observed  in  the  revolution  of  the  moon  round  the  earth,  and 
of  the  planets  round  the  sun. 


CENTRAL   MOTION.  159 

If  we  suppose  the  point  a  (Fig.  135),  to  have  received  an  im- 
pulse in  the  direction  a  b  from  any  momen- 
tarily acting  force  at  the  beginning  of  its 
course,  while  it  is  driven  towards  the  point 
m  by  a  constantly  acting  force  of  attraction, 
it  will  neither  move  in  the  directions  a  b  nor 
a  c,  but  in  another  direction  a  d,  which  may 
be  ascertained  by  the  law  of  the  parallelo- 
gram of  forces.  In  order  to  make  the  con- 
sideration more  simple,  we  will  assume  that 
the  constantly  attracting  force  directed  towards  m,  acts  by  im- 
pulses at  short  intervals,  and  this  will  be  found  the  more  nearly 
to  approach  the  truth,  the  smaller  we  imagine  these  intervals  to 
be.  If  the  laterally  directed  impulse  alone  would  drive  the  ma- 
terial point  in  a  short  space  of  time  t  from  a  to  b,  and  the  attract- 
ing force,  acting  alone,  would  urge  it  in  the  same  time  to  c,  it 
would  move  under  the  influence  of  both  forces  in  the  instant  of 
time  t,  from  a  to  d.  Arrived  at  c?,  it  would  move  further  in  the  direc- 
tion de,  and  in  the  time  t,  the  space  de  would  be  exactly  as  great 
as  a  d,  if  the  attracting  force  did  not  act  again  in  such  a  manner, 
as  if  the  body  had  received  an  impulse  in  d,  which,  acting  alone, 
would  have  led  it  in  the  time  t  from  d  iof.  By  this  second  action 
of  the  attracting  force,  the  body  is  again  turned  from  the  direction 
d  e,  and  urged  to  g. 

From  this  we  can  easily  understand,  that  if  the  body  have  re- 
ceived at  a  a  laterally  directed  impulse,  while  the  attracting  force 
acts  at  small  intervals,  it  must  describe  a  polygon,  which  ap- 
proaches more  nearly  to  a  curved  line  in  proportion  to  the  small- 
ness  of  the  intervals.  When  the  attracting  force  constantly  acts, 
as  it  does  in  nature,  the  course  will  truly  be  a  curved  line,  the 
nature  of  which  will  depend  upon  the  relation  of  the  influencing 
forces. 

The  force  that  constantly  urges  a  body  towards  a  central  point 
of  attraction,  is  designated  the  centripetal  force.  If,  at  any  mo- 
ment, the  centripetal  force  were  to  cease  acting,  the  body  would 
from  that  instant  continue  to  move  in  the  direction  of  a  tangent, 
and  the  force  thus  acting  is  named  the  tangential  force. 

The  figure  described  by  the  course  of  a  body  will  be  a  circle, 
an  ellipsis,  &c.,  according  to  the  relation  between  the  tangential 
and  centripetal  forces. 


160 


CENTRAL    MOTION. 


Fig.  136. 


Let  us  seek  to  determine  the  amount  of  the  centripetal  force, 
that  urges  the  moon  in  its  motion  round  the  earth  towards  the 
central  point  of  the  latter.  The  earth's  circumference  is  40  mil- 
lions of  metres  (24,880  miles);  but  as  the  radius  of  the  moon's 
orbit  is  equal  to  60  radii  of  the  earth  (237,600  miles),  the  circum- 
ference of  the  moon's  orbit  is  2400  millions  of  metres  (1,493,485 
miles).  This  course  it  traverses  in  27  days,  7  hours,  43  minutes, 
or,  what  is  the  same  thing,  in  39,343  minutes.  In  every  minute, 

therefore,  the  moon  passes  over  a  space  of  ?12P>OQO'QQO=6 1,000 

39,343 

metres  (66,810  yds.).  Fig  136  represents  the  arc  a  b  of  61,000 
metres,  traversed  by  the  moon  in  one  mi- 
nute ;  a  c  is,  therefore,  the  amount  of  space 
through  which  the  moon  would  approach 
the  earth  in  one  minute  by  the  force  of 
gravity,  if  the  action  of  the  tangential  force 
were  suddenly  destroyed. 

We  may  compute  the  magnitude  of  the 
distance  a  c,  by  assuming  that  the  arc  a  b 
is  a  straight  line,  from  which  it  actually 
deviates  but  slightly  ;  a  b  n  is  then  a  right 
angled  triangle,  b  c  is  a  perpendicular  let 
fall  from  the  right  angle  upon  the  hypo- 
thenuse;  and,  under  such  circumstances, 
in  accordance  with  a  known  proposition  of 
geometry,  a  b  is  a  mean  proportional  be- 
tween a  c  and  a  n\  consequently 


and  hence 


ab* 

a  c  —  — 
an 


Now  we  have  seen  that  a  6=61,000ra;  but  a  n,  the  radius  of  the 
moon's  orbit,  is  763,950,000m.  If  we  put  this  value  in  the  place 
of  a  b  and  an  into  the  last  equation,  we  have 

a  c  =4,87  , 

that  is,  we  find  the  attraction  of  the  moon  towards  the  earth 
amounts  to  4,87  metres  in  a  minute. 

But  what  is  the  force  producing  this  action?  Is  it  the  same 
force  that  makes  the  stone  fall  to  the  earth?  If  we  assume  that 
the  force  of  gravity  observed  upon  the  surface  of  the  earth,  extends 


CENTRAL    MOTION.  161 

its  influence  beyond  our  atmosphere,  acting  even  on  the  moon, 
we  can  easily  comprehend  that  its  intensity  must  diminish  with 
the  distance  from  the  earth.  By  a  simple  mode  of  deduction, 
which  we  shall  consider  more  attentively  when  we  treat  of  light, 
we  find  that  the  intensity  of  all  actions  emanating  from  one  point 
stands  in  an  inverse  relation  to  the  squares  of  the  distance.  Con- 
sequently, at  double,  triple,  quadruple  the  distance  from  the 
earth's  centre,  the  intensity  of  the  force  of  gravity  will  be  dimin- 
ished 4,  9,  16  times. 

At  the  moon  it  is,  therefore,  602  or  3600  times  weaker  than  at 
the  surface  of  the  earth,  because  the  moon  is  removed  60  times 
farther  from  the  earth's  centre.  If,  according  to  this,  the  space 
fallen  through  in  the  first  second  on  the  earth's  surface  were  4,9 
metres,  the  space  fallen  through  by  the  moon  towards  the  earth  in 

4  9 

one  second  would  be  —  metres,  and  consequently  in  a  minute, 
602 

4  9 
that  is  sixty  seconds,  it  would  be  -^-.  602  =  4,9  metres.  That 

is  the  space  by  which  the  moon  approaches  the  earth  in  one 
minute  must  be  as  great  as  the  space  fallen  through  in  the  first 
second  of  fall  upon  the  earth's  surface. 

If  we  compare  the  space,  viz.,  4,9  metres,  calculated  for  the 
fall  of  the  moon  towards  the  earth  in  a  minute,  with  the  4,87 
metres  deduced  from  astronomical  observations,  we  shall  really  only 
find  a  very  small  difference,  which  would  wholly  disappear  if  we 
had  not,  for  the  sake  of  the  simpler  computation,  taken  only 
approximating  values  into  consideration.  Thus  we  have  entirely 
neglected  the  seconds  in  giving  the  time  of  the  moon's  revolution, 
and  have  assumed  the  distance  of  the  moon  from  the  earth  to  be 
equal  to  60,  although  it  really  is  60,16  radii  of  the  earth. 

In  this  manner  the  motion  of  the  planets  round  the  sun  may  also 
be  explained,  and  it  is  thus  one  and  the  same  force  that  urges  the 
stone  to  the  earth,  and,  acting  through  the  whole  space  of  the  hea- 
vens, maintains  the  harmony  of  our  planetary  system. 

For  the  knowledge  of  this  vast  law  of  general  gravity,  we  are 
indebted  to  the  penetration  and  the  unwearying  industry  of 
Newton.  Had  he  done  nothing  more,  this  single  discovery  would 
have  sufficed  to  immortalize  his  name. 

In  the  same  manner  in  which  we  have  developed  the  amount  of 
the  centripetal  force  in  the  motion  of  the  moon,  we  may  also 

14* 


162  CENTRAL   MOTION. 

obtain  a  general  expression  for  these  forces.  Let  us  assume,  as  a 
measure  of  the  centripetal  force,  the  space  a  c,  through  which  the 
body  in  its  central  motion,  in  a  unit  of  time,  will  be  urged  towards 
the  centre  of  attraction,  and  let  us  designate  it  by  p\  then,  as  has 

T  o 

been  already  proved,  p  = .    Now  the  arc  a  &  is  that  which  the 

an 

body  actually  describes  in  the  unit  of  time,  therefore,  a  b  = -, 

If 

if  r  be  the  radius  of  the  spherical  orbit,  and  t  designate  the  time  of 
revolution.  Further,  an  is  the  diameter  of  this  orbit,  and  conse- 
quently equals  2r.  If  we  substitute  these  values  of  a  b  and  a  n 
in  the  above  equation,  we  find  that 


n  = 


t* 

That  is  to  say:  if  two  bodies  move  in  different  orbits,  and  with 
different  times  of  revolution,  the  centripetal  forces  will  be  as  the 
radius  of  the  circles  described)  and  inversely  as  the  squares  of  the 
times  of  revolution. 

If  a  small  sphere,  which  we  must  suppose  devoid  of  weight,  be 
fastened  to  the  end  of  a  string  at  m,  and  turned  round  the  point  c, 
so  that  it  describes  a  circle  round  the  centre 
c,  the  string  will  constantly  have  to  sustain 
..•'•'"  \         a  tension  increasing  with  the  speed  of  the 

revolution.  If,  at  any  moment,  the  string 
were  severed,  the  ball,  instead  of  moving  on 
in  a  circle,  would  by  reason  of  its  inertia  fly 
off  at  a  tangent  from  its  former  path. 

The  cause  of  the  tension  sustained  by  the 
string  is  designated  centrifugal  force. 
But  as  the  resistance  of  the  string  produces  the  same  effect  as 
the  centripetal  force  considered  under  the  head  of  central  motion, 
it  is  clear  that  the  centrifugal  force  is  equal,  and  opposed  to  the 
centripetal  force,  and  that  all  that  has  been  said  of  the  latter 
applies  equally  to  the  former,  that  is,  that  the  centrifugal  force 
increases  in  the  ratio  of  the  radius  of  the  orbit,  and  inversely  to  the 
square  of  the  period  of  revolution.  As  a  matter  of  course  the 
tension  of  the  string,  and  consequently  the  centrifugal  force,  must 
be  proportional  to  the  revolving  mass. 

Centrifugal  force  prevails  wherever  there  is  a  rotation  round  a 
fixed  axis,  and  the  separate  particles  are  prevented  in  any  way 


OF    THE   PENDULUM.  163 

deviating  from  this  axis.  Such  a  centrifugal  force  must,  therefore, 
be  occasioned  by  the  rotation  of  the  earth  round  its  axis.  As  the 
time  of  rotation  is  the  same  for  all  points  of  the  earth,  while  the 
different  points  are  not  equi-distant  from  the  axis  of  rotation,  it  is 
clear  that  this  centrifugal  force  is  not  equal  upon  the  earth's  sur- 
face, but  must  be  as  the  distances  from  the  earth's  axis ;  conse- 
quently, it  is  at  its  minimum  at  the  poles,  and  at  its  maximum  at 
the  equator. 

This  centrifugal  force  which  is  greatest  at  the  equator,  and 
diminishes  as  it  approaches  the  poles,  acts  against  gravity,  and 
lessens  its  intensity.  We  may  easily  compute  the  amount  of 
velocity  with  which  the  earth  must  rotate  on  its  axis,  in  order  that 
the  centrifugal  force  engendered  at  the  equator  may  fully  counter- 
act the  effect  of  gravity. 

The  .apparatus  represented  at  Fig.  138,  is  particularly  well  cal- 
culated for  experiments  con- 
cerning the  centrifugal  force. 
We  will,  however,  limit  our- 
selves to  one  experiment, 
explaining  the  flattening  of 
the  earth  at  the  poles. 

By  help  of  the  handle  m, 
the  horizontal  disc  below  it 
is  made  to  revolve.  The 
rotation  of  the  disc  is  trans- 
mitted by  the  thread  d  to 
another  disc  of  a  smaller  radius.  It  will  of  course  be  evident 
that  the  smaller  disc  must  make  more  revolutions  than  the  larger 
one  in  the  same  period  of  time,  these  bearing  the  same  relation 
to  each  other  as  the  radii  of  the  two  discs.  The  vertical  axis  c, 
fastened  in  the  middle  of  the  smaller  disc,  turns  with  it.  A  spring 
a  b  fastened  by  its  lower  end  to  the  axis,  but  admitting  of  its 
other  extremity  being  freely  moved  up  and  down,  and  which  in  a 
state  of  rest  forms  a  spherical  figure,  will  by  rapid  revolution 
assume  an  elliptical  form,  owing  to  the  centrifugal  force  acting 
with  the  greatest  intensity  upon  those  points  of  the  spring  that  are 
the  furthest  removed  from  the  axis. 

Of  the  Pendulum. — The  common  pendulum  consists  of  a  heavy 
ball  suspended  to  the  end  of  a  flexible  thread.  If  we  disturb  the 
equilibrium  of  the  pendulum,  that  is  if  we  remove  it  from  its 


164      LAWS    OF    THE    OSCILLATIONS    OF    THE    PENDULUM. 

vertical  position,  it  will,  when  left  to  itself  and  without  receiving 

any  impulse,  continue  to  oscillate  in  a 

Fig.  139.  .,•      i       i  rr-  i     •          ,n 

f.  vertical  plane.     If  we  bring  the  pen- 

dulum into  the  position  f  a,  the  ball 
will  describe  an  arc  a  I,  reaching  /  with 
such  velocity  as  to  be  carried  forward 
as  high  as  b  on  the  other  side,  that  is 
to  say  to  the  elevation  of  the  point  a ; 
from  6,  the  pendulum  again  traverses 
in  a  reversed  direction  the  arc  b  I  «, 
and  in  this  manner  continues  its  oscil- 
lations. The  velocity  of  the  pendulum 
constantly  increases  with  its  descent  and  diminishes  with  its 
ascent ;  at  the  moment,  therefore,  in  which  the  pendulum  passes 
the  point  of  equilibrium  it  has  attained  its  greatest  velocity. 

The  motion  from  a  to  6,  or  from  b  to  a  is  termed  an  oscillation, 
from  a  to  /  is  a  semi-descending  oscillation,  from  /  to  b  a  semi- 
ascending  oscillation. 

The  amplitude  of  an  oscillation,  is  the  magnitude  of  the  arc  a  b 
expressed  in  degrees,  minutes,  and  seconds. 

The  time  of  an  oscillation  is  the  time  necessary  for  the  pendu- 
lum to  traverse  this  arc. 

At  the  first  glance  we  might  conclude  from  this  experiment 
that  the  motions  of  a  pendulum  must  always  continue,  for  if 
starting  from  a  it  be  borne  up  to  an  equal  height  b  on  the  other 
side,  it  must,  starting  from  b,  also  ascend  to  #,  and  thus  continue 
the  same  course,  a  second,  third,  and  fourth  time,  and  thus  on  to 
eternity. 

This  deduction  would  be  perfectly  correct,  if  b  were  absolutely 
at  an  equal  elevation  with  a ;  but  the  friction  at  the  point  of  sus- 
pension/, and  the  resistance  of  the  air  that  must  be  displaced  by 
the  ball,  hinder  the  latter  from  ascending  exactly  to  the  same 
height  from  which  it  descended.  This  difference  becomes  only 
appreciable  after  a  series  of  oscillations,  and  instead  of  wondering 
that  the  motion  does  not  continue  for  ever,  we  ought  rather  to  be 
surprised  that  it  lasts  so  long,  for  a  pendulum  can  go  on  oscillat- 
ing for  hours  together. 

Laws  of  the  Oscillations  of  the  Pendulum. — The  laws  of  the 
oscillations  of  simple  pendulums,  are  as  follows : 


LAWS    OF    THE    OSCILLATIONS    OF    THE    PENDULUM.      165 

1.  The  duration  of  the  oscillation  is  independent  of  the  weight 
of  the  ball  and  the  nature  of  its  substance. 

To  prove  this,  we  must  construct  several  pendulums  of  equal 
length,  the  ball  of  one  being  of  metal,  of  another  wax,  of  a  third 
wood,  &c.,  and  we  shall  then  find  that  all  have  equal  durations  of 
oscillation. 

When  gravity  makes  a  pendulum  oscillate,  it  acts  upon  every 
atom  of  the  matter  composing  the  ball;  each  atom  of  the  ball  is 
acted  upon  by  its  own  gravity,  and  consequently  an  increase  of 
the  atoms  can  have  no  influence  on  the  velocity  of  the  oscillations. 
If  we  could  suspend  a  single  atom  of  iron  to  a  thread  devoid  of 
weight,  it  must  oscillate  just  as  fast  as  if  we  attached  to  it  two  or 
three  atoms,  or  even  a  ball  of  iron.  Gravity,  however,  might  act 
otherwise  upon  a  molecule  of  wax  than  upon  a  molecule  of  iron. 
That  it  does  not  do  so,  that  gravity  acts  alike  on  a  molecule  of 
gold,  platinum,  wax,  iron,  &c.,  is  proved  by  the  experiment  with 
the  pendulum.  The  already  mentioned  experiment  on  falling  in 
a  vacuum  is  but  a  rough  illustration  of  the  fact,  as  we  have  only 
to  observe  the  action  of  gravity  during  an  extremely  short  period 
of  time.  The  pendulum,  however,  enables  us  to  watch  the  in- 
fluence of  gravity  upon  different  bodies  during  many  hours  toge- 
ther. 

2.  The  duration  of  small  oscillations  of  the  same  pendulum  is 
independent  of  their  magnitude.     If,  for  example,  a  pendulum 
vibrates  4 — 5°,  the  duration  of  the  oscillation  is  the  same  as  if  it 
vibrated  only  1°. 

This  law  may  be  thus  developed.  If  the  angle  of  deviation  be 
not  too  large,  the  inclination  of  the 
course  towards  the  horizon  will  be  pro- 
portionate to  the  distance  from  the 
point  of  equilibrium.  If  we  suppose 
a  tangent  drawn  at  c  to  the  arc  of  the 
circle,  it  will  form  an  angle  with  the 
horizon  twice  as  great  as  the  angle 
made  with  the  horizon  by  the  tangent 
at  c',  provided  the  arc  c'  a  be  half  as 
great  as  the  arc  c  a.  If,  therefore,  the 
pendulum  begin  its  motion  at  c,  the 
accelerating  force  is  twice  as  great  as  when  it  begins  its  descent 


166      LAWS    OF    THE    OSCILLATIONS    OF    THE    PENDULUM. 

from  c';  the  arc  c  d  which  we  will  assume  to  be  so  small  that  ill 
may  be  considered  a  straight  line,  and  the  arc  cf  d'  only  half  the  I 
size,  will,  therefore,  be  traversed  in  an  equal  period  of  time,  i  I 
motion  begin  at  one  time  in  c,  and  at  another  in  c'. 

If  we  suppose  two  equal  pendulums  suspended  to  an  axis,  the'i 
one  raised  to  c,  the  other  to  c',  and  both  going  off  simultaneously. ; 
they  will  reach  the  points  d,  and  df  at  the  same  time.     But  the 
accelerating  force  at  d  is  twice  as  great  as  that  at  df,  besides  which, 
the  pendulum  reaches  a  point  d  with  twice  as  great  a  velocity  as 
that  with  which  the  other  passes  the  point  d',  and  hence  it  follows, 
that  also  in  the  next  short  interval  of  time,  the  one  pendulum  will 
have  traversed  twice  as  much  space  as  the  other.     By  pursuing 
this  mode  of  deduction',  we  at  last  find  that  both  pendulums  must 
arrive  simultaneously  at  a. 

This  reasoning  may  also  be  applied  if  the  relation  of  the  angle 
of  deviation  be  not  exactly  between  1 — 2°,  since  the  accelerating 
force  is  always  proportionate  to  the  distance  from  the  position  of 
equilibrium  for  small  angles  of  deviation ;  and  thus  it  may  gene- 
rally be  proved,  that  within  certain  limits  the  deviation  of  the 
oscillation  is  independent  of  the  magnitude  of  the  angle  of  devia- 
tion. 

In  order  to  confirm  this  law  by  experiment,  we  must  accurately 
determine  the  time  necessary  for  a  pendulum  to  make  several 
hundred  oscillations. 

If  this  observation  be  made  at  the  beginning  of  the  motion, 
when  the  amplitude  is  4 — 5°,  subsequently  when  it  only  amounts 
to  2 — 3G;  and  lastly  when  the  oscillations  have  become  so  small 
as  to  require  the  aid  of  the  lens  for  detecting  them,  we  shall  find 
that  the  oscillations  are  truly  isochronous  at  these  three  stages. 

3.  The  durations  of  the  oscillations  of  two  pendulums  of  un- 
equal length  are  as  the  square  roots  of  the  lengths  of  the  pen- 
dulums. 

We  must  suppose  the  arc  a  b  described  by  the  oscillation  of  a 
pendulum  to  be  divided  into  so  many  parts  that  each  division  may 
be  considered  as  a  straight  line.  If  now  the  angle  of  deviation  of 
a  longer  pendulum  is  equally  large,  the  arc  of  oscillation  c  d  must 
be  to  the  arc  of  oscillation  a  b  as  the  lengths  of  the  pendulums  to 
each  other.  If  we  suppose  the  arc  d  c  to  be  divided  in  an  equal 
number  of  parts  as  the  arc  a  6,  these  separate  parts  will  be  to  each 


LAWS    OF    THE    OSCILLATIONS    OF    THE    PENDULUM.      167 


other  as  the  lengths  of  the  pendulums.     If,  Fis- 14L 

therefore,  one  pendulum  be  four  times  longer 
than  the  other,  the  subdivisions  of  the  arc  d  c 
will  also  be  four  times  larger  than  those  cor- 
responding divisions  of  the  arc  a  b.  The 
angles  made  with  the  horizon  by  the  first, 
second,  and  third  divisions  of  the  arc  a  6,  are 
equal  to  the  angles  made  with  the  horizon  by 
the  first,  second,  and  third  divisions  of  the 
arc  c  c?;  the  accelerating  force  is,  therefore, 
also  the  same  on  the  corresponding  parts  of  a  b  and  c  d. 

But  if  different  spaces  be  traversed  with  equal  accelerating 

forces,  we  know  from  the  formula  s  =  °    t2,  that  the  times  of 

falling  are  as  the  square  roots  of  the  spaces;  if,  therefore,  each  of 
the  parts  of  c  d  were  two,  three,  or  four  times  as  large  as  the  cor- 
responding divisions  of  a  6,  the  time  in  which  a  division  of  c  d 
will  be  traversed,  must  also  be  \/2,  >/3,  \/4,  \/n  times  as  long 
as  the  period  occupied  in  traversing  the  corresponding  portions  of 
a  b.  But  as  this  is  true  of  all  the  parts,  so  it  is  also  true  of  their 
sums,  or,  in  other  words,  the  duration  of  the  oscillation  is  propor- 
tionate to  the  square  root  of  the  length  of  the  pendulum. 

In  order  to  confirm  the  accuracy  of  this  third  law  by  experi- 
ment, we  will  take  three  pendulums  of  different  lengths.  If,  for 
instance,  the  lengths  are  as  the  numbers  1,  4,  9, 
the  corresponding  times  of  oscillation  will  be  as  the 
numbers  1,  2,  3.  The  most  convenient  mode  of 
exemplifying  this,  is  by  attaching  the  balls  to  a 
double  thread  as  seen  in  the  accompanying  figure. 
While  a  pendulum  four  feet  in  length  makes  one 
oscillation,  the  pendulum  which  is  four  times  smaller 
than  the  former  makes  two  oscillations,  and  whilst 
a  pendulum,  one  foot  in  length  moves  three  times 
backwards  and  forwards,  another,  nine  feet  long, 
will  only  make  one  backward  and  forward  motion. 

The   length   of  a   simple   pendulum  oscillating 
seconds,  is  994  millimetres ;  if,  therefore,  the  length 
of  a  second's  pendulum  had  been  taken  as  the  unit  of  length,  it 
would  have  deviated  but  little  from  the  metre. 


Fig.  142. 


168  QUANTITY    OF    MOTION. 

Quantity  of  Motion. — Most  forces  that  set  bodies  in  motion  act 
only  directly  upon  a  small  portion  of  the  molecules  composing  the 
body.  In  striking  a  billiard-ball  we  only  touch  a  few  points  of 
the  surface.  If  the  wind  drive  a  ship,  it  only  presses  upon  the 
sails,  and  when  a  ball  is  discharged  by  powder,  the  gases  which 
give  the  impulse  on  being  liberated,  press  only  upon  half  the 
surface  of  the  ball.  Notwithstanding  this,  all  parts  of  the  body 
move,  whether  they  be  directly  acted  upon  or  not.  Motion  must, 
therefore,  be  uniformly  distributed  to  all  the  molecules,  as  all 
move  simultaneously.  The  molecules  directly  struck,  impart  an 
impulse  to  those  nearest  them,  and  so  on,  until  the  whole  mass  is 
set  in  motion.  A  certain,  although  inappreciably  small  portion 
of  time  is  necessary  for  the  transmission  of  motion  from  one  mole- 
cule to  the  whole  mass. 

If  a  force  act  upon  a  body,  it  will  have  produced  its  effect  as 
soon  as  motion  has  been  distributed  to  all  portions  of  the  mass, 
and  these  latter  move  with  a  common  velocity,  the  force  being 
then  transferred,  as  it  were,  to  the  body,  and  diffused  through  it. 

If,  therefore,  a  body  be  projected  by  the  hand,  by  the  release 
of  a  spring,  by  a  quick  push,  or  by  means  of  a  sudden  explosion, 
it  will  continue  to  move  on  after  the  force  has  ceased  to  act  upon 
it.  If  nothing  were  to  oppose  it  in  its  course,  neither  air,  water, 
nor  any  other  body,  and  if  no  force  whatever  were  acting  upon  it, 
it  would  move  in  the  direction  of  the  first  impulse  with  uniform 
velocity  after  a  hundred  years  in  the  same  manner  that  it  did  after 
the  first  second.  We  may  say  that  the  activity  of  such  a  body  is 
momentary,  while  its  effect  lasts  for  ever. 

Thus  the  body  to  a  certain  extent  absorbs  the  force  acting 
upon  it,  and  we  can,  therefore,  easily  understand  how  the  same 
force  acting  upon  different  bodies  must  call  forth  very  different 
motions. 

A  quantity  of  powder,  sufficient  to  discharge  a  musket-ball, 
would  scarcely  raise  a  bomb;  while  a  bow  capable  of  sending  a 
light  arrow  to  a  great  distance,  would  not  be  able  to  send  off  a 
heavy  one  with  as  much  speed.  We  say  commonly  that  the 
gravity  of  the  body  gives  rise  to  this  difference,  but  this  is  an 
incorrect  assertion,  since  we  might  be  erroneously  led  to  conclude 
that  if  a  body  were  to  cease  to  be  heavy,  the  same  force  would 
move  all  bodies  with  equal  velocity.  Let  us  suppose,  for  a  mo- 
ment, that  bodies  are  without  gravity,  and  assume  that  there  is 


QUANTITY    OF    MOTION.  169 

no  air  present,  or  other  hinderance  of  motion ;  the  musket  ball 
would  still  be  urged  on  faster  than  the  bomb,  because  the  same 
force  must  produce  a  degree  of  speed,  smaller  in  proportion  as 
the  mass  of  matter  to  be  moved  increases  in  size.  It  is  one  of  the 
fundamental  principles  of  machines,  that  the  same  force,  acting 
upon  different  bodies,  imparts  to  them  a  velocity  inversely  propor- 
tionate to  their  masses ;  that  is  to  say,  in  an  inverse  ratio  to  the 
quantities  of  matter  composing  them.  If,  therefore,  the  same  force 
discharged  in  succession  leaden  balls,  whose  volumes,  and  like- 
wise whose  masses  were  as  the  numbers  1,  2,  3,  4,  &c.,  it  would 
impart  to  them  the  velocities  1,  J,  J,  J,  &c.,  so  that  a  mass  ten 
times  larger  would  only  have  TVth  the  velocity.  On  multiplying 
each  of  these  masses  with  its  velocity,  we  always  obtain  the  same 
product  for  the  first  1  X  1  =  1  for  the  second  2  X  J  =  1,  &c. 
The  quantity  thus  obtained  by  multiplying  a  body  by  its  velocity 
is  termed  quantity  of  motion.  The  same  force  also  produces 
always  the  same  quantity  of  motion  on  whatever  body  it  acts. 

In  order  to  obtain  a  clear  idea  of  the  mode  of  action  of  various 
machines,  we  must  compare  the  quantity  of  motion,  which  the 
applied  force  is  capable  of  producing,  with  the  effect  obtained  by 
means  of  the  machine.  It  would  be  a  vulgar  error  to  regard  a 
machine  as  a  source  of  force,  or  to  believe  that  the  quantity  of 
motion  could  be  increased  by  machinery.  By  machines  the  nature 
of  the  motion  is  simply  changed,  without  its  quantity  being  in  the 
least  increased  thereby. 

A  weight  of  twenty-five  pounds  may  be  easily  lifted  two  feet 
and  a  half  in  a  second,  by  means  of  a  rope  swung  round  a  simple 
pulley.     But  if  the  rope,  pulled  by  the  workman,  were  passed 
round  a  wheel  (Fig.   143),   and  the 
load  attached  to  an  axle  of  four  times 
smaller   diameter,    a    fourfold    larger 
weight  might  be  raised  by  an  equal 
application  of  force,  although  with  a 
speed  four  times  smaller.     If  we  ex- 
amine the   mode  of  action  of  other 
machines,  as  the  screw,  the  pulleys  of 
various  wheel  works,  we  shall  always 
attain  to  the  same  results,  viz.,  that 
what  we  gain  on  the  one  side  in  force, 
15 


170  THE    MATERIAL    rENDULTM. 

Ave  lose  on  the  other  in  speed,  and  that  consequently  the  quantity 
of  motion  is  not  at  all  increased  by  machines. 

If  a  body  in  motion  come  into  contact  with  another  at  rest,  but 
which  is  easily  moved,  it  will  impart  to  the  latter  a  portion  of  its 
motion;  but  the  total  quantity  of  motion  is  not  thereby  altered; 
and  if  the  striking  body  rebound  in  consequence  of  elasticity,  and 
the  impulse  were  centrally  applied,  both  bodies  will  move  on  in 
the  same  direction  after  coming  into  contact.  If  the  mass  of  the 
body  at  rest  be  equal  to  that  of  the  one  striking  it,  the  speed  of 
motion  will  be  diminished  to  the  half  after  contact,  as  the  mass 
has  been  doubled.  From  this  we  may  easily  see  that,  in  order  to 
find  the  relation  of  the  speed  before  contact  to  that  of  the  speed 
subsequently  manifested,  we  have  only  to  divide  the  mass  of  the 
body  moved  by  the  sums  of  the  masses  of  the  body  moved  and 
the  body  at  rest.  If,  for  instance,  a  musket  ball  of  ?V  Ib.  wr 
strike,  with  a  speed  of  1300  feet  in  a  second,  a  ball  of  48  Ibs.  at 
rest,  but  easily  movable  and  suspended  to  a  long  line,  the  com- 
mon speed  after  the  blow  would  be  to  1300  as  »V  is  to  48  -f  ^V* 

1  '300 
or  as  1  to  961  ;  that  is,  it  would  be  only  about  -    —  or  about  1  J 


feet  in  a  second. 

If  a  similar  musket  ball  were  to  strike  against  a  large  block  of 
stone  or  a  rock,  it  would  also  impart  a  motion  to  it,  but  the  speed 
would  be  very  inconsiderable;  for,  if  the  block  of  stone  were 
500  Ibs.,  the  common  speed  after  the  contact,  as  may  easily  be 
reckoned,  would  be  only  one  inch  in  the  second.  But  friction, 
however,  soon  destroys  this  motion,  which  by  degrees  distri! 
itself  to  all  neighboring  bodies,  and  finally  to  the  whole  earth, 
and  thus  entirely  disappears. 

Motion,  therefore,  distributes  itself  to  other  bodies,  but  is  not 
lost.     If  it  appear  wholly  destroyed,  the  reason  is,  that,  b\ 
gradual  distribution  to  other  bodies,  it  finally  becomes  imper- 
ceptible.    Motion  is  necessary  to  destroy  motion;  resistance  only 
scatters  without  destroying  it. 

The  (material)  Pendulum.  —  The  above  developed  laws  apply, 
strictly  speaking,  only  to  an  ideal  pendulum.      Such  a  pendu- 
lum we   may  conceive,  but  we   cannot   construct,  for   it   must 
consist  of  a  simple  thread  devoid  of  all  weight,  and  having  a 
extremity  only  a  heavy  point. 

Every  pendulum  not  corresponding  with  both  these  conditions 


THE  MATERIAL   PENDULUM.  171 

is  a  compound  pendulum.  An  inflexible  rod  devoid  of  weight  on 
which  are  two  heavy  molecules,  m  and  n,  would  consequently  be 
a  compound  pendulum. 

The  molecule  m  nearer  to  the  point  of  suspension  than  n,  has 
a  tendency  to  vibrate  more  rapidly,  but  as  both  molecules  are 
combined,  m  will  hasten  the  motion  of  n,  and  conversely  n  will 
retard  that  of  m\  the  vibrations  will,  on  that 
account,  move  with  a  velocity  varying  between  j 

the  degrees  of  velocity  with  which  each  of  the 
molecules  m  and  n  would  oscillate  alone.    They 
are  equal  to  the  oscillations  of  a  simple  pendu- 
um  longer  thanf  m,  and  shorter  ihanfn.     It 
s  the  same  with  every  material   pendulum.         / 
Fhose  parts  lying  nearest  the  central  point  of       j 
ribration  in  the  pendulum  have  their  motion      / 
•etarded  by  the  most  remote,  while  the  latter     •'•-. — 
e  accelerated  by  the  parts  most  contiguous 
the  point  of  suspension.    There  must,  consequently,  be  a  point 
every  compound  pendulum,  which  is  not  acted  upon  by  the 
st  of  the  mass  of  the  pendulum,  vibrating  exactly  as  fast  as  a 
mple  pendulum,  whose  length  is  equal  to  its  distance  from  the 
int  of  suspension.     This  is  called  the  centre  of  oscillation.     If 
e  speak  of  the  length  of  a  compound  pendulum,  we  understand 
f  the  term  the  distance  of  this  point  from  the  point  of  suspension, 
,  what  is  the  same  thing,  the  length  of  a  simple  pendulum  of  an 
[ual  time  of  oscillation. 

A  pendulum,  consisting  of  a  fine  thread,  at  whose  lower  end  a 
dl,  or  a  double  cone,  of  a  substance  of  great  specific  gravity,  is 
tached,  approaches  most  nearly  to  the  simple  pendulum.  If  the 
read  be  somewhat  long,  and  the  diameter  of  the  ball  somewhat 
nail,  in  proportion  to  the  length  of  the  pendulum,  wre  may,  without 
y  serious  error,  take  the  centre  of  gravity  of  the  ball  as  the  point 
oscillation  of  the  pendulum,  or,  in  other  words,  we  may  take 
ich  a  pendulum  for  a  simple  one. 

In  every  actual  pendulum,  however,  which  differs  more  consider- 
)ly  from  the  form  of  a  simple  pendulum,  the  centre  of  gravity  is 
IT  no  means  the  centre  of  oscillation  ;  it  is,  in  most  cases,  a  diffi- 
ilt  problem  to  ascertain  by  calculation  where  the  centre  of  oscil- 
tion  lies  in  an  actual  pendulum,  because,  in  a  computation  of 
is  kind,  we  must  not  only  have  regard  to  the  accelerating  force 


172  THE   PENDULUM    CLOCK. 

of  gravity  of  the  individual  points  lying  at  different  distances  from 
the  point  of  suspension,  but  also  to  the  resistance  opposed  to  an 
acceleration  of  motion  owing  to  the  inertia  of  their  mass. 

The  simplest  way  of  seeing  that  the  centre  of  oscillation  of  an 
actual  pendulum  cannot  coincide  with  its  centre  of  gravity,  is  by 
observing  a  pendulum  in  which  a  portion  of  the  mass  lies  above 
the  point  of  suspension.  Such  a  pendulum  vibrates  considerably 
slower  than  it  would  do,  if  its  centre  of  gravity  were  the  centre  of 
oscillation. 

Fig.  145  represents  an  evenly  divided  rod,  provided  in  the  middle 
Fig  H5     w^  an  ec*£e  sim*lar  to  what  forms  the  fulcrum  of  the 
beam  of  a  balance.     If,  now,  we  fasten  a  leaden  mass, 
weighing  two  pounds,  one  decimetre  above,  and  another 
of  the  same  weight  equally  far  below  this  edge,  and 
place  the  edge  upright  on  its  support,  the  rod  with  its 
weights  will  be  in  a  condition  of  indifferent  equilibrium, 
for  the  centre   of  gravity  of  the    system   corresponds 
with  the  fulcrum ;  as  soon,  however,  as  we  attach  a 
small  extra  weight  to  the  lower  end  of  the  rod,  the 
whole  becomes  a  pendulum.     But  the  oscillations  of 
this  pendulum  are  much  slower  than  those  of  a  simple 
pendulum  of  the  length  a  /,  for  the  only  force  that  sets 
the  whole  system  in  motion  is  the  gravity  of  the  lower 
leaden  weight ;  this,  however,  has  not  only  its  own  mass 
to  move,  but  also  the  masses  of  the  weights  at  c  and  d. 
We  thus  easily  perceive  why  the  beam  of  a  balance,  which  may 
be  considered  as  a  pendulum,  vibrates  so  slowly,  although  its  centre 
of  gravity  is  close  to  the  point  of  suspension,  and  why  it  must 
vibrate  very  rapidly  if  the  centre  of  gravity  were  really  the  centre 
of  oscillation. 

The  Pendulum  Clock. — The  most  important  application  of  the 
pendulum  is  for  the  regulation  of  clocks.  Every  clock  must  have 
an  accelerating  force  to  produce  and  maintain  motion.  From 
what  has  been  said,  however,  concerning  accelerating  forces,  it  is 
evident,  that,  if  some  other  equal  force,  or  hinderance  of  motion, 
do  not  oppose  the  accelerating  force,  motion  cannot  remain  uniform, 
but  will  become  faster  and  faster,  as  in  a  falling  body.  In  our 
large  upright  clocks,  this  accelerating  force  is  produced  by  weights, 
hung  to  a  line  passed  round  a  horizontal  axle.  If  the  weight  be 
drawn  down  by  its  gravity,  the  axle  will  be  turned  by  the  line,  and 


THE   PENDULUM   CLOCK. 


173 


the  whole  machinery  set  in  motion.  But  the  motion  of  a  falling 
weight  is  an  accelerating  one ;  consequently  the  check  must  at 
first  go  slowly,  then  more  and  more  quickly,  unless  its  course 
were  regulated,  and  this  regulation  is  effected  by  means  of  the 
pendulum.  * 

Fig.  146  exhibits  the  manner  in  which  the  pendulum  regulates 
the  going  of  a  clock.     A  toothed  wheel  is  fastened  to  the  axis  to 


Fig.  146. 


which  the  line  with  the  weight 
is  attached.  The  axis,  round 
which  the  pendulum  vibrates,  is 
above  this  wheel,  and  to  this 
axis  is  secured  a  beam  a  6, 
which  catches  the  teeth  of  the 
wheel  on  either  side.  The 
figure  represents  the  pendulum 
in  the  position  where  it  is  at 
the  extreme  left  side.  The 
wheel  is  turned  by  the  weight 
in  the  direction  of  the  arrow, 
but  cannot  go  on,  having  the 
tooth  1  held  by  the  tooth  6  of 
the  lever :  as  soon,  however,  as 
the  pendulum  vibrates  back 
again,  b  rises,  and  the  tooth  1 
is  suffered  to  pass  ;  but  the  mo- 
tion of  the  wheel  is  again  im- 
mediately arrested,  because  the 
tooth  a  at  the  other  end  of  the 
lever  now  descends,  pressing 
against  the  tooth  2  of  the  wheel : 
thus  the  wheel  can  move  one 
tooth  at  every  oscillation,  and  the 
same  every  time  the  pendulum 
returns,  and  thus  the  motion  of 
the  wheel  is  regulated  by  the 
movements  of  the  pendulum.  Such  a  contrivance  is  called  an 
escapement. 

In  watches,  the  weight  is  replaced  by  a  tensely  drawn  steel 
spring,  and  the  pendulum  by  a  fine  spring  vibrating,  owing  to  its 
elasticity,  round  its  point  of  equilibrium.  Clocks  made  in  Paris, 

15* 


174  IMPEDIMENTS    TO    MOTION. 

and  which  there  went  quite  well,  were  found  to  lose  when  brought 
near  the  equator,  so  that  it  was  necessary  to  shorten  their  pendu- 
lums. Hence  it  follows  that  the  same  pendulum  goes  more  slowly 
at  the  equator  than  near  the  poles,  and  consequently,  that  the  action 
of  gravity  is  less  at  the  equator  than  at  the  poles.  This  is  owing 
to  two  causes  :  first,  the  flattening  of  the  earth ;  and  secondly,  the 
centrifugal  force  produced  by  its  rotation  round  its  axis,  and  which 
is  stronger  at  the  equator. 

Impediments  to  Motion. — A  resistance  already  often  spoken 
of,  and  which  exercises  a  considerable  influence  upon  almost  all 
motions,  is  friction.  In  order  to  propel  a  load  of  moderate  size 
along  a  horizontal  plane,  a  considerable  application  of  force  is 
necessary,  arising  entirely  from  the  resistance  of  friction.  If  the 
plane,  on  which  the  mass  is  to  be  propelled,  as  well  as  the  under 
surface  of  the  load,  be  perfectly  hard  and  smooth,  (which  is 
never  the  case  in  nature,)  the  smallest  force  might  set  a  very  large 
mass  in  motion,  and  once  impelled,  the  load  would  move  on  with 
uniform  speed  on  the  horizontal  plane. 

Friction  arises,  incontestably,  from  the  elevations  of  one  of  the 
surfaces  entering  into  the  depressions  of  the  latter.  If,  now, 
motion  is  to  occur,  the  projecting  parts  must  be  torn  away  from 
the  mass  of  the  body,  or  the  one  body  must  be  continually  lifted 
over  the  inequalities  of  the  other.  The  first  occurs  if  one  or  both 
the  rubbing  surfaces  are  very  rough.  If,  however,  the  rubbing 
surfaces  can  possibly  be  smoothed,  the  last  named  mode  of  action 
almost  exclusively  takes  place. 

The  accompanying  figure  may  serve  to  explain  the  manner  in 
Fi    147  which  resistance  to  motion  arises, 

if  a  body  must  be  lifted  over 
small  inequalities.  The  lifting  of 
the  body  A  is  effected  by  raising 
the  lowest  points  of  the  projections 
of  A  to  the  summit  of  the  inequa- 
lities of  the  under  layer,  whence 
they  must  again  slide  down,  and 

the  same  raising  and  lowering  be  repeated.  The  resistance  op- 
posed here  by  Ji  to  the  motion,  is  no  other  than  what  must  be 
overcome  to  draw  it  up  an  entirely  smooth  inclined  plane. 

If  this  view  of  friction  be  correct,  the  laws  relating  to  it  must 
admit  of  being  proved  by  experiment. 


IMPEDIMENTS    TO   MOTION.  175 

In  order  to  overcome  friction,  we  must,  exactly  as  in  drawing 
the  body  up  an  inclined  plane,  apply  a  force  equal  to  an  aliquot 
part  of  the  load.  The  number  that  gives  the  relation  of  the  force 
to  the  weight  is  termed  the  co-efficient  of  friction.  It  naturally 
depends  upon  the  peculiarities  of  the  rubbing  surfaces,  and  can  be 
determined  by  experiment. 

If,  for  instance,  we  would  propel  a  load  of  one  cwt.  upon  a 
horizontal  layer  of  iron  (on  the  line  of  a  railroad,  for  instance),  and 
if  the  under  surface  of  the  truck  were  also  iron,  a  force  of  27,7  Ibs. 
would  be  necessary  ;  that  is  to  say,  the  same  expenditure  of  force 
that  would  be  requisite  for  lifting  27,7  Ibs.  vertically  up.  When 
iron  rubs  on  iron,  the  resistance  of  friction  is,  as  we  see,  27,7  per 
cent.  ;  and  the  co-efficient  of  friction,  in  this  case,  is  0,277.  In  order 
to  ascertain  the  co-efficient  of  friction  for  different  bodies,  we  may 
make  use  of  an  apparatus  as  seen  at  Fig.  10.  The  board  R  S  is 
placed  in  a  horizontal  position.  Suppose  this  board  to  be  of  oak, 
we  lay  a  block  of  oak  upon  it,  whose  under  surface  must  also  be 
well  planed,  weighing  1000  grammes  (15,444  grs.);  a  line  is 
attached  to  this  block  of  oak,  and  passed  round  a  pulley  as  in  the 
experiments  of  the  inclined  plane,  carrying  a  light  scale-pan. 
This  latter  will  not  be  sufficient  to  produce  motion,  wrhich  will  not 
begin  before  the  weight  of  the  scale-pan,  and  of  the  weights  toge- 
ther, amount  to  418  grammes  (6,456  grs.).  We  obtain,  by  this 
experiment,  the  co-efficients  of  friction  of  oak  upon  oak,  and  find 
them  to  be  0,418. 

If  we  alter  the  substance  of  the  body  to  be  moved,  as  well  as  of 
the  body  supporting  it,  we  may  ascertain  the  co-efficient  of  friction 
of  different  bodies.  The  following  table  contains  some  of  the  most 
practically  important  co-efficients  of  friction. 

Iron  upon  iron  ....  0,277 
Iron  upon  brass  ....  0,263 
Iron  upon  copper  ....  0,170 

(  0,418  = 
Oak  upon  oak          .         .         . 


Oak  upon  pine        ....  0,667 
Pine  upon  pine       ....  4,562 

The  resistance  of  friction  maybe  diminished  by  the  application 
of  well  chosen  oleaginous  substances.  Oil  is  the  best  for  metal, 
while  tallow  answers  best  for  wood. 


176  IMPEDIMENTS    TO    MOTION. 

In  woods  it  is  by  no  means  a  matter  of  indifference  which  way 
the  fibres  run ;  friction  is  much  less  considerable  where  they  run 
across  (+)  than  where  they  are  parallel  (=). 

From  what  has  been  said,  it  is  directly  shown  that  friction  is 
always  proportionate  to  the  weight.  If,  for  instance,  in  the  above 
experiment,  we  had  taken  a  block  of  oak  weighing  2000  grammes 
(30,888  grs.),  we  should  have  had  to  attach  836  grammes  (12,912 
grs.)  to  the  rope,  in  order  to  overcome  the  friction. 

The  size  of  the  surface  in  contact  cannot,  according  to  the  above 
views,  exert  any  influence  on  the  amount  of  friction  ;  this  may  be 
also  proved  by  experiment.  Suppose  that  the  block  of  wood  have 
lateral  surfaces  of  different  size,  no  difference  will  be  found  in  the 
result,  whichever  surface  of  the  block  touch  the  wood. 

The  above  described  kind  of  friction  is  termed  sliding  friction, 
in  order  to  distinguish  it  from  the  rolling  friction,  which  we  pro- 
ceed to  consider  more  attentively. 

Sliding  friction  always  occurs  where  pins  or  axes  revolve  in  their 
supports.  In  order  the  better  to  take  into  account  the  effect  of 
friction  in  this  case,  we  need  only  consider  that  it  acts  precisely 
like  a  corresponding  weight  suspended  to  a  string  passed  round  the 
same  axle.  Let  us,  by  way  of  illustration,  examine  the  effect  of 
friction  on  the  windlass.  Let  the  weight  of  the  axle,  with  every 

thing  that  is  fastened  to  it,  be  about 
751bs.,  the  stone  to  be  raised  100 Ibs., 
and  the  force  acting  on  the  circum- 
ference of  the  wheel,  be  25  Ibs.,  then 
the  combined  pressure  sustained  by 
the  props  of  the  axle  will  be  75  + 
100  +  25  =  200  Ibs.  If  the  props 
be  of  brass,  but  the  extremities  of  the 
axle  be  of  iron,  the  resistance  of  fric- 
tion acting  on  the  circumference  of  the 
ends  of  the  axle,  will  be  26,3  per  cent.;  the  effect  of  friction  is, 
therefore,  the  same  as  if  in  place  of  this  we  had  passed  a  line 
round  the  ends,  in  the  same  direction  as  the  line  bearing  the 
weight,  and  had  attached  to  it  a  weight  200  X  0,263,  or  52,6  Ibs., 
or  as  if  the  load  acting  at  the  circumference  of  the  axle  had  been 

52  6 

—£-   or  10,5  Ibs.  larger,  provided  that  the  diameters  of  the  rods 
o 

were  y  of  that  of  the  axle.     Thus  about  10  per  cent,  of  the  force 


IMPEDIMENTS    TO   MOTION.  177 

applied,  is  lost  in  this  windlass,  in  overcoming  the  resistance  of 
friction. 

It  now  remains  to  notice  rolling  friction.  Rolling  friction  occurs 
where  a  round  body,  as  a  ball,  or  a  cylinder,  rolls  along  a  surface. 
Here  the  supporting  under  surface  comes  always  in  contact  with 
new  points  of  the  rolling  body.  The  resistance  that  arises  here  is 
by  far  less  than  the  resistance  of  sliding  friction,  as  may  be  seen 
from  the  following  consideration. 

If  we  wish  to  propel  the  round  body  Jl  over  the  surface  on 
which  it  rests,  we  must  begin  by  drawing  it  to  a  little  inclined 
plane  c  b,  when  its  centre  of  gravity 
will  be  raised  as  much  as  c  lies  below  Flg' 149> 

b.  But  by  rolling  on  the  body  ./?,  it 
will  turn  round  the  point  5,  by  which 
its  centre  of  gravity  will  only  be  raised 
from  d  to  e.  The  difference  of  height, 
however,  between  d  and  e,  is  much 
less  than  the  difference  of  height  be- 
tween c  and  b.  Let  us  suppose  a  spheri- 
cal arc  to  be  drawn  round  the  central 
point  d,  and  through  the  points  a  and  6, 
the  lowest  point  of  this  arc  will  be  as  much  below  &,  as  d  is  below 
e.  But  as  the  lowest  point  of  the  arc  a  b  still  lies  high  above  c, 
we  may  easily  understand  that  the  alternate  rising  and  falling  of 
the  centre  of  gravity,  is  much  less  considerable  in  rolling  than  in 
sliding  friction.  We  also,  however,  perceive  that  the  resistance 
of  friction  depends  mainly  here  upon  the  radius  of  the  rolling 
body.  The  larger  this  radius  is,  the  smaller  will  be  the  resistance. 
In  other  respects,  resistance  is  here  likewise  proportionate  to  the 
load. 

In  the  wheel  of  a  carriage  there  is  rolling  friction  at  the  cir- 
cumference of  the  wheel,  but  sliding  friction  at  the  axles.  Both 
resistances  become  smaller  in  proportion  to  the  larger  diameter  of 
the  wheels. 

In  both  kinds  of  friction,  adhesion  has  considerable  influence. 

In  a  locomotive,  the  middle  wheels,  the  so-called  driving  wheels, 
are  turned  by  the  force  of  the  steam-engine ;  the  whole  carriage 
rolls  on  in  consequence  of  this,  for,  if  it  were  to  remain  at  rest,  the 
wheels  could  not  revolve  without  the  occurrence  of  a  considerable 
sliding  friction  between  the  wheels  and  the  iron  on  which  they 


178  IMPEDIMENTS    TO   MOTION. 

ran,  whilst  by  rolling  on,  the  incomparably  smaller  rolling  friction 
has  alone  to  be  overcome.  If  a  locomotive  be  attached  to  a 
number  of  carriages,  a  certain  resistance  of  friction  must  be 
overcome  during  the  continuance  of  motion — rolling  friction  at 
the  circumference,  and  sliding  friction  at  the  axles.  All  these 
resistances  must  be  overcome  if  the  carriage  is  to  be  drawn 
onward. 

It  is  evident  that  the  number  of  oarriages  attached,  might,  at 
last,  be  so  increased,  that  the  locomotive  would  no  longer  be  able 
to  draw  them ;  in  this  case,  therefore,  the  wheels  of  the  locomotive 
would  revolve  without  its  being  borne  forward,  when  the  con- 
siderable friction  of  the  sliding  friction,  at  the  circumference  of 
the  driving  wheels,  would  have  to  be  overcome  by  the  force  of 
the  machine. 

The  train,  therefore,  can  only  proceed  if  the  sum  of  all  the 
resistances  of  friction  of  all  the  carriages  is  smaller  than  the 
resistance  of  the  sliding  friction  from  the  rotation  of  the  driving 
wheels  of  the  locomotive  at  the  circumference  which  would  exist 
were  there  no  forward  motion. 

From  these  considerations,  it  follows,  that  the  load  which  a 
locomotive  is  capable  of  drawing,  depends  not  only  upon  the 
force  of  its  steam-engine,  but  always  upon  its  weight.  If  we  as- 
sume that  two  locomotives  have  equally  strong  machines,  but  that 
the  one  is  heavier  than  the  other,  a  larger  weight  may  be  pro- 
pelled by  the  heavier  of  the  two. 


LAWS   OF   THE   MOTION   OF    LIQUIDS.  179 


CHAPTER    II. 

LAWS  OF  THE  MOTION  OF  LIQUIDS. 

IF  we  make  an  opening  in  the  lateral  wall,  or  the  bottom  of  a 
vessel  filled  with  liquid  and  open  at  the  top,  and  if  the  aperture 
thus  made  be  small  in  comparison  with  the  dimensions  of  the  ves- 
sel, the  liquid  will  flow  out  with  a  velocity  whose  intensity  will  be 
in  proportion  to  the  depth  of  the  opening  below  the  surface  of  the 
liquid.  The  connection  existing  between  the  velocity  of  the 
escaping  liquid,  and  the  height  of  the  pressure,  may  be  most 
simply  expressed  in  the  following  manner: — The  velocity  of  the 
escaping  liquid  is  exactly  as  great  as  the  velocity  a  freely  falling 
body  would  acquire,  if  it  were  to  fall  from  the  surface  of  the  liquid 
to  the  aperture  through  which  the  liquid  escapes. 

This  proposition  is  known  by  the  name  of  the  Toricellian 
theorem.  It  may  be  explained  in  the  following  manner : 

If  the  liquid  layer  abed  (Fig.  150)  imme- 
diately above  the  opening  a  b,  were  to  fall  down 
without  being  accelerated  by  the  liquid  pressing 
over  it,  it  would  flow  from  the  opening  with  a 
velocity  corresponding  to  the  height  a  c,  which 
we  will  designate  as  h.  This  velocity  is  c  =  %/ 
2  g  h.  But  now  the  escaping  stratum  is  not  only 
accelerated  by  its  own  gravity,  but  by  the  gravity 
of  all  the  liquids  pressing  upon  it.  The  accele- 
rating force  of  the  gravity  g  is,  consequently,  to  the  accelerating 
force  gfy  actually  propelling  the  liquid  particles,  as  a  c  is  to  af, 
or  as  h  is  to  s  if  the  height  of  pressure  be  designated  by  s,  that  is 

h  :  s  =  g  :  g1, 
and,  therefore,  the  accelerating  force  gf,  acting  upon  the  liquid 

layer  flowing  out,  is  =  £-  s.  But  if  the  accelerating  force  acting 
h 

upon  this  layer  be  g'  and  not  g,  then  its  velocity  c'  =  \/  2  gf  h-} 


180 


THE    VELOCITIES    OF    EFFLUX. 


and  if  we  add  the  value  of  g'  to  this  value  of  c',  we  obtain  as  the 
value  of  the  velocity  of  the  escaping  fluid 
c'  =  N/  2  g  s. 

But  this  is  the  same  velocity  as  that  acquired  by  a  body  falling 
freely  from  a  height  s. 

From  this  proposition  it  immediately  follows  that : 

1.  The  velocity  of  the  efflux  depends  only  upon  the  depth  of  the 
aperture  below  the  surface,  and  not  upon  the  nature  of  the  liquid. 
At  equal  heights  of  pressure,  water  and  mercury  will,  therefore, 
flow  out  with  equal  velocity.     Every  layer  of  mercury  will  cer- 
tainly be  driven  out  by  a  pressure  13,6  times  greater  than  that 
acting  on  water,  but  then  the  mass  of  a  particle  of  mercury  is 
13,6  times  heavier  than  that  of  an  equally  large  particle  of  water. 

2.  The  velocities  of  efflux  are  as  the  square  roots  of  the  heights  of 
pressure.     The  water  must,  therefore,  flow  with  ten  times  greater 
velocity  from  an  opening  100  inches  below  the  level  of  the  liquid, 
than  from  a  depth  of  only  one  inch  below  the  same  level. 

In  order  to  determine  the  velocity  of  efflux,  the  simplest  way  is 
to  observe  a  jet  issuing  vertically  or  horizontally  from  the  vessel. 
We  will  first  consider  the  vertically  directed  jet. 

If  the  water  spring  forth  from  the  opening  o  (Fig.  151)  with  the 

same  velocity  as  if  it 


Fig.  151, 


Fig.  152. 


were  to  fall  from  the 
level  of  the  liquid  in 
the  vessel  to  the  height 
of  the  opening  0,  the 
jet  of  water  must  rise 
again  to  the  elevation 
of  the  liquid-level.  We 
may  easily  show  this 
by  the  help  of  the  ap- 
paratus represented  in 
Fig.  152,  letting  the 
water  flow  from  the 
opening  c;  and  we  shall 
then  find  that  the  as- 
cending jet  of  water 
does  not  attain  to  anything  like  the  height  that  might  be  expected. 
The  impediments  to  motion  are,  however,  the  sole  cause  of  the 
water  not  attaining  the  height  yielded  by  theory ;  the  water  fall- 


THE    VELOCITIES    OF    EFFLUX.  181 

ing  back  from  the  top  exerts  an  essential  influence  in  hindering 
the  free  ascent  of  the  succeeding  water;  and  consequently  the 
jet  rises  the  higher,  immediately  the  aperture  of  efflux  is  so  turned, 
that  the  water  flowing  out  may  make  a  small  angle  with  the  ver- 
tical, that  is,  that  the  ascending  and  descending  jets  may  be  close 
to  each  other.  In  this  case,  the  jet  may,  under  favorable  circum- 
stances, that  is,  where  there  is  the  smallest  possible  friction,  attain 
an  elevation  0,9  of  the  height  of  the  pressure. 
.  A  stream  of  water  flowing  out  in  a  horizontal  direction  describes 
a  parabola,  the  form  of  which  depends  upon  the  velocity  of  its 
efflux.  Supposing  that  the  p.  153 

opening  a  (Fig.  153)  were 
0,lm  below  the  water  level, 
the  velocity  of  efflux  would  be 
.according  to  the  Toricellian 
law,  v/ 2.9,8.0,1  =  l,4m.  If, 
therefore,  a  particle  of  water 
were  at  any  moment  to  flow 
from  the  opening,  it  would  in 
one  second  be  l,4m  from  the 
vertical  wall  of  the  vessel,  and  0,28ra  in  ^  of  a  second.  But  in 
0,2  of  a  second,  the  water  falls  0,196™  (we  find  this  on  substitut- 
ing the  value  0,2  for  1  in  the  equation  s—  H  t2) ;  if  now  we  mea- 

2 

sure  the  length  a6=0,196m  downwards  from  the  opening  a, 
a  horizontal  line  drawn  from  b  towards  the  jet  of  water  will 
intersect  the  latter  at  a  distance  of  0,28m.  In  making  the  experi- 
ment, the  distance  b  c  will  be  somewhat  less  than  0,28m,  owing  to 
the  action  of  friction. 

According  to  theory,  the  water  should  flow  from  a  second 
opening  d  40cm,  below  the  surface,  with  a  velocity  double  that  at 
a;  if,  therefore,  we  measure  196mm  from  d  downward,  and  then 
suppose  a  horizontal  line  drawn  towards  the  jet,  it  must  intersect 
the  latter  at  a  distance  of  0,56m. 

The  quantity  of  water  issuing  from  an  opening,  in  a  given  time, 
depends  evidently  upon  the  size  of  the  opening,  and  the  velocity 
of  the  efflux.  If  all  the  particles  of  water  passed  the  opening  with 
the  velocity  corresponding  according  to  the  Joricellian  law  with 
the  height  of  the  pressure,  the  water  flowing  out  in  one  second 
would  form  a  cylinder  whose  base  would  be  equal  to  the  opening, 
16 


182  THE    VELOCITIES    OF    EFFLUX. 

and  its  height  equal  to  the  distance  described  by  a  particle  of 
water  (owing  to  its  velocity)  in  a  second.  This  distance  is,  how- 
ever, the  velocity  of  the  efflux  itself,  and  therefore,  \/2gs9  and 
designating  the  area  of  the  opening  by/,  the  quantity  expelled 
in  a  second  will  be 


If  we  assume  that  the  apertures  m  and  n  are  circular,  and  that 
their  diameter  is  5mm,  the  area  of  the  opening/=  19,625  square 
millimetres,  or  0,19625  square  centimetres,  if  the  height  of  the 
pressure  be  ten  centimetres,  the  velocity  of  the  efflux  will  be  as 
we  have  already  computed  1.4m  =  140cn%  and  therefore 
m=  0,19625  X  140  =  27,475  cubic-  centimetres. 

In  a  minute,  therefore,  1648,5  cubic-centimetres,  or  148,5 
cubic-centimetres,  more  than  1J  litres  must  flow  out. 

An  aperture  of  equal  size  lying  40cm  below  the  water-level, 
must  yield  double  as  much  in  one  minute  ;  that  is,  3  litres  and 
297  cubic-centimetres  of  water. 

If  we  make  the  experiment,  we  find  that  the  upper  opening  only 
yields  about  1  litre  and  55  cubic-centimetres,  and  the  lower  one 
2  litres  and  110  cubic-centimetres. 

This  difference,  between  the  theoretical  and  the  actually  ob- 
served quantity  of  the  discharge,  proves  incontrovertibly  that  all 
the  particles  of  water  do  not  pass  the  aperture  with  a  velocity 
corresponding  to  the  height  of  the  pressure.  In  fact  it  is  only 
those  particles  of  water  lying  in  the  centre  of  the  opening  that 
have  this  velocity,  while  that  of  the  particles  flowing  nearer  to 
the  edge  of  the  opening,  is  much  less  considerable,  as  we  shall 
see  from  the  following  observations. 

[The  experiments  of  Bossut  show  that  the  actual  quantity  of 
water  discharged  from  orifices  of  the  same  dimensions,  under  dif- 
ferent degrees  of  pressure,  is  much  less  than  is  inferred  by  calcu- 
lation; this  is  exemplified  in  the  following  table: 

Weight  of  fluid     Computed  discharge  per     Actual  discharge 
above  the  orifice,     minute  in  cubic  inches.         per  minute.  Per  cent. 

1  foot  4,427  2,812  63.5 

5  feet  10,123  6,277  62.0 

10     "  14,317  8,860  61.8 

15     "  17,533  10,821  61.1  ] 

In  a  wide  vessel  having  a  narrow  opening,  the  whole  liquid 
mass,  with  the  exception  of  the  parts  in  the  vicinity  of  the  aper- 


INFLUENCE    OF    CONDUCTING    TUBES.  183 

ture,  may  be  regarded  as  at  rest.  The  layers  that  successively 
flow  out,  do  not  begin  their  motion  simultaneously,  the  foremost 
having  attained  the  maximum  of  their  velocity,  whilst  the  most 
bsrckward  are  beginning  their  motion.  The  consequence  of  this 
would  be  a  breaking  up  of  the  successive  layers  if  vacua  could 
be  formed;  as  this,  however,  cannot  occur,  the  separate  layers 
become  more  elongated  while  their  diameter  diminishes ;  but  in 
the  proportion  that  the  diameter  of  these  layers  diminishes,  other 
particles  of  water  must  flow  on  from  the  sides  ;  as  these,  however, 
only  begin  later  their  motion  at  right  angles  to  the  opening,  it  is 
clear  that  they  must  reach  the  opening  with  less  velocity  than  the 
central  lines  of  water. 

Whilst  the  nucleus  of  the  jet  has  a  velocity  corresponding  to 
the  height  of  the  pressure  at  the  moment  of  its  leaving  the  aper- 
ture, it  is  surrounded  by  lines  of  water,  whose  velocity  diminishes 
in  proportion  as  they  approach  the  edge  of  the  aperture:  whence 
it  follows,  that  the  quantity  flowing  out  must  be  less,  than  if  all 
the  particles  left  the  opening  with  the  velocity  of  the  nucleus  of 
the  jet. 

The  water  flowing  out  is  not  perfectly  cylindrical,  but  contracted 
at  the  opening  as  seen  in  Fig.  154,  in 
consequence  of  the  central  lines  of  water  Fls- 154- 

at  their  passage  through  the  opening 
having  a  greater  velocity  than  the  parts 
near  the  edges,  and  in  consequence  of 
the  latter  being  possessed  of  a  velocity 
directed  towards  the  centre  of  the  jet. 
At  c  d  the  diagonal  section  of  the  stream 
is  about  equal  to  two-thirds  of  the  area  of 
the  opening.  In  like  manner  the  actual 
quantity  of  water  expelled  is  about  two-thirds  of  the  theoretical. 

Influence  of  conducting  tubes  upon  the  quantity  of  liquid  dis- 
charged.— If  the  efflux  does  not  take  place  through  openings 
made  in  a  thin  wall,  but  through  short  tubes,  remarkable  modifi- 
cations occur,  which  we  purpose  considering. 

If  a  conducting  tube  have  exactly  the  form  of  the  free  jet  from 
the  opening  to  the  part  where  the  latter  contracts,  and  exactly 
the  length  between  these  two  points,  it  will  exercise  no  influence 
upon  the  quantity  of  liquid  discharged. 

In  cylindrical  pipes,  the  water  either  pours  freely  out  as  from 


184  INFLUENCE    OF    CONDUCTING    TUBES. 

an  opening  of  equal  diameter,  in  which  case  no  influence  is  exer- 
cised upon  the  quantity  of  liquid,  or  the  water  adheres  to  the 
walls  of  the  pipes,  so  that  the  liquid  fills  the  whole  pipe,  and 
flows  forth  in  a  stream  having  the  diameter  of  the  pipe ;  in  this 
case  the  pipe  considerably  influences  the  quantity  discharged. 
Whilst  an  opening  in  a  thin  wall  yields  theoretically  0.64  of 
liquid,  wre  obtain  by  such  a  cylindrical  conducting  pipe  of  like 
diameter  84  p.  c.,  provided  the  length  of  the  pipe  is  equal  to  four 
times  its  diameter.  The  stream  always  adheres  to  the  pipes  at 
lower,  while  it  is  free  at  greater  pressures.  Where  there  is  a 
medium  pressure,  it  may  be  made  free  or  adherent  at  pleasure ; 
an  inconsiderable  impediment  will  occasion  adhesion,  while  a 
very  slight  touch  is  often  sufficient  to  render  the  stream  free. 

A  conical  conducting  pipe  acts  in  case  it  discharges  when  full, 
in  the  same  manner  as  a  cylindrical  pipe,  excepting  that  it  occa- 
sions an  increased  efflux. 

The  speed  of  the  efflux  is  diminished  in  cylindrical  or  conical 
conducting  pipes  in  the  same  proportion  as  the  quantity  of  dis- 
charge is  increased. 

We  must  now  examine  how  it  happens  that  conducting  pipes 
increase  the  quantity  of  liquid  discharged,  while  on  the  contrary 
they  diminish  the  velocity  of  the  efflux. 

The  water  suffers  a  contraction  on  entering  the  conducting 
pipe,  in  the  same  manner  as  if  it  were  discharged  from  an  open- 
ing in  a  thin  wall,  but  besides  this,  as  soon  as  the  walls  of  the 
pipe  are  wetted,  adhesion  acts  in  such  a  manner  on  these  walls 
that  the  conducting  tubes  become  entirely  filled,  and  the  diagonal 
section  of  the  stream  thus  increases,  being  at  its  exit  from  the 

pipe  larger  than  at  the  place  of  con- 
Fig.  155.  Fig.  156.  traction,  as  may  be  seen  at  Fig.  155. 
That  such  a  contraction  actually  oc- 
curs in  the  tube  is  proved  by  this,  that 
if  we  give  the  conducting  tube  the 
shape  of  a  contracted  stream  as  in 

Fig.  156,  the  efflux  is  precisely  the  same  as  if  the  conducting 
tube  were  cylindrical. 

If  the  particles  of  water  filling  the  whole  section  of  the  tube 
leave  it  with  the  same  velocity  with  which  they  pass  the  most 
contracted  part,  a  breaking  up  of  the  succeeding  layers  of  water 
must  necessarily  occur.  The  separation  of  the  particles  of  water, 


LATERAL    PRESSURE    OF    LIQUIDS    IN    MOTION.  185 

and  consequently  the  formation  of  vacua  is,  however,  hindered  by 
the  pressure  of  the  air  which  accelerates  the  motion  of  the  liquid 
while  flowing  into  the  tube,  but  retards  its  efflux  from  it.  By 
atmospheric  pressure,  the  particles  of  water  flowing  out  are  so 
much  retarded  that  a  full  efflux  is  produced. 

That  the  pressure  of  the  air  really  has  this  effect  is  especially 
proved  by  the  quantity  of  the  discharge  not  being  increased  by 
putting  on  conducting  pipes  where  water  flows  into  a  vacuum. 

If  we  make  a  hole  in  the  lateral  wall  of  a  conducting  pipe,  the 
air  will  be  drawn  in  through  this  opening,  and  the  stream  will 
cease  to  be  continuous. 

If  a  bent  tube  x  y,  Fig.  155,  whose  lower  end  opens  into  a 
vessel  of  water,  be  inserted  into  the  lateral  wall,  the  water  in  the 
tube  x  y  will  be  sucked  up  by  the  tendency  manifested  by  the 
water  to  form  a  vacuum  in  the  conducting  pipe.  This  pheno- 
menon proves  likewise  the  influence  exercised  by  the  air  in  the 
above  experiments.  As  a  conical  conducting  pipe  gives  a  larger 
discharge  than  one  that  is  cylindrical,  it  must  also  draw  up  more 
liquid,  that  is,  under  otherwise  similar  conditions,  the  column  of 
water  drawn  into  the  tube  x  y  by  a  conical  conducting  pipe  will 
rise  to  a  greater  height  than  in  a  cylindrical  pipe. 

Lateral  pressure  of  liquids  in  motion. — If  water  flow  through 
pipes  out  of  a  reservoir,  the  lateral  walls  of  the  pipes  would  not 
have  to  support  any  pressure,  if  there  were  no  resistance  of  friction 
to  overcome ;  this,  however,  under  some  circumstances  may  be  so 
considerable,  that  the  greater  part  of  the  hydrostatic  pressure  is 
lost  in  overcoming  this  resistance,  and  proves  of  no  avail  in  aiding 
the  motion. 

Instead  of  the  plate  with  the  opening  c  in  Fig.  152,  let  us  insert 
into  the  apparatus  a  cork,  in  which  is  a  glass  tube  three  feet  in 
length,  and  give  the  tube  a  horizontal  direction,  when  the  water 
at  the  end  of  the  tube  will  then  flow  out  much  more  slowly  than 
if  the  efflux  had  occurred  through  the  opening  c. 

If  we  apply  several  equally  long  tubes  of  different  diameters  to 
exhibit  this  experiment,  we  shall  see  how  the  velocity  of  the  dis- 
charge diminishes  with  the  narrowness  of  the  tubes. 

Supposing  we  find  that  the  velocity  of  the  efflux  for  one  of  these 
tubes  is  only  half  as  great  as  we  should  expect  from  the  amount  of 
height  of  the  pressure,  then  the  one-half  of  this  pressure  is  neces- 

16* 


186      REACTION    CREATED    BY    THE    EFFLUX    OF    LIQUIDS. 


Fig.  157. 


sary  to  overcome  the  friction,  and  the  other  half  only  is  available 

for  motion.  If  the  water  in 
the  tube  a  c  (Fig.  157)  were 
to  move  with  a  velocity  cor- 
responding to  the  height  of 
the  pressure  in  the  reservoir, 
the  walls  of  the  tubes  would 
have  no  pressure  to  support; 
but  if  the  water  in  the  reservoir 
produces  in  the  tube  a  motion 
corresponding  only  to  a  part 
of  the  height  of  the  pressure, 
the  remainder  must  act  upon 
the  walls  of  the  tubes  as  hydrostatic  pressure.  The  pressure  sus- 
tained by  the  walls  is,  however,  not  equal  in  all  parts  of  the  tube, 
being  less,  the  nearer  it  approaches  the  opening  c.  In  many 
cases,  the  pressure  to  be  supported  by  the  walls  of  the  tubes  from 
within  may  be  less  than  the  pressure  of  air  acting  upon  them  from 
without;  this  is  everywhere  the  case  where  the  conditions  are 
fulfilled  in  which  the  phenomenon  of  suction  occurs. 

Reaction  created  by  the  efflux  of  Liquids. — If  we  suppose  a 
vessel  filled  with  water,  the  whole  will  be  at  rest,  as  every  lateral 
pressure  is  counteracted  by  a  perfectly  equal,  but  opposite  one. 
But  if  we  make  an  opening  at  any  part  of  the  wall  from  which 
the  water  may  flow  forth,  the  pressure  will  evidently  be  removed 
at  this  spot,  whilst  the  portion  of  the  wall  diametrically  opposite 
and  corresponding  to  it  will  be  pressed  upon  as  strongly  as  before. 
The  pressure,  therefore,  on  the  wall  of  a  vessel  through  which  the 
opening  has  been  made,  is  less  than  that  acting  on  the  opposite 
side,  consequently  the  whole  vessel  must  move 
in  a  direction  opposed  to  the  direction  in  which 
the  stream  of  water  flows  out,  if  this  motion  be 
not  hindered  by  friction  or  some  other  cause. 
This  may  be  compared  to  the  recoil  of  fire- 
arms. The  reaction  manifested  on  the  escape 
of  water  may  be  shown  by  an  apparatus  known 
by  the  name  of  Segner's  Water-wheel.  It  con- 
sists of  a  vessel  v  turning  round  a  vertical 
axis,  and  having  at  its  upper  extremity  a  cock 
r,  which  need  only  be  turned  in  order  to  put 


Fig.  158. 


REACTION    CREATED    BY    THE    EFFLUX    OF    LIQUIDS.      187 

the  apparatus  into  motion.  By  means  of  the  reaction  of  the 
streams  of  water,  issuing  from  the  end  of  the  horizontal  and 
curved  tubes  t  and  tf,  and  at  a  tangent  to  the  circle  described 
by  the  end  of  the  tubes,  the  apparatus  receives  a  rapid  rotatory 
motion. 

Vertical  Water-wheels. — If  water  continually  flow  from  a  more 
highly  elevated  to  a  lower  spot,  it  may  be  applied  as  a  moving 
force. 

If  during  a  unit  of  time,  as  a  second,  a  mass  of  water  whose 
weight  is  M,  flow,  or  fall  from  a  height  h,  M  h  is  the  quantity  of 
motion,  or  the  mechanical  moment  of  this  mass  of  water.  In 
whatever  way  we  may  turn  the  motion  of  the  water  to  another 
body,  the  effect  can  never  exceed  the  mechanical  momentum  of 
the  fall,  that  is,  we  can  by  means  of  the  fall,  at  most  raise  to  an 
equal  height,  a  weight  equal  to  the  mass  of  water  falling  from  the 
same  height  in  the  same  unit  of  time,  or  effect  some  other  similar 
action.  If,  for  instance,  a  mass  of  water  of  800  Ibs.  fell  from  a 
height  of  twenty-four  feet  in  one  second,  the  absolute  maximum 
of  the  effect  of  this  fall  is  19,200,  that  is,  a  result  might  be  pro- 
duced by  this  fall,  supposing  all  forces  to  come  into  action  without 
there  being  any  loss  by  friction  or  other  resistance,  which  would 
be  equal  to  the  force  necessary  to  raise  a  weight  of  19,200  Ibs. 
in  one  second  to  an  elevation  of  one  foot. 

If  we  assume  that  a  horse  working  with  medium  force  and 
medium  speed  can  raise  a  load  of  100  Ibs.,  four  feet  in  one  second, 
the  absolute  maximum  of  the  effect  of  that  fall  might  be  compared, 
or  would  be  equal  to  a  forty- eight  horse-power.  In  what  follows, 
we  will  designate  the  absolute  maximum  of  a  fall  by  the  letter  E. 

In  order  to  avail  ourselves  of  the  mechanical  momentum  of  a 
water-fall,  we  generally  make  use  of  water-wheels,  that  is  wheels, 
on  the.  circumference  of  which  the  water  acts  by  means  of  pres- 
sure or  impact. 

Ordinary  water-wheels  turn  in  a  vertical  plane  round  a  hori- 
zontal axis.  We  distinguish  three  main  kinds  of  vertical  water- 
wheels,  under-shot,  over-shot  and  middle-shot. 

In  under-shot  wheels  the  float-boards  are  at  right  angles  with 
the  circumference  of  the  wheel.  The  lowest  float-boards  are  im- 
mersed in  the  water,  which  flows  with  a  velocity  depending  upon 
the  height  of  the  fall. 

The  flowing  water  sets  the  wheel  in  motion,  and  imparts  to  it 


188  VERTICAL    WATER-WHEELS. 

a  velocity  which  may  be  greater  or  smaller  according  to  circum- 
stances. 

If  the  impact  of  the  water  is  to  impart  to  the  wheel  a  velocity 
equal  to  that  with  which  the  water  would  flow  if  there  were  no 
wheel,  there  must  be  no  resistance  opposed  by  the  wheel  to  this 
motion,  it  must  therefore  not  be  loaded ;  or  in  this  case  there  can 
be  no  mechanical  action  produced,  and  the  effect  will  be  null. 

On  the  other  hand,  we  might  load  the  wheel  so  strongly  by  a 
counterpoising  weight,  that  the  strike  of  the  water  would  not 
impart  any  motion  to  it,  the  falling  water  exercising  only  a  static 
pressure,  and  keeping  the  whole  in  equilibrium.  In  this  case,  the 
effect  is  also  null.  From  this  consideration  it  follows  that  where 
the  wheel  is  to  do  any  work,  it  must  move  with  a  velocity  less 
than  that  of  the  freely  flowing  water;  theory  and  experience  showT 
that  the  most  advantageous  effect  is  produced,  if  the  velocity  of 
the  wheel  be  half  as  great  as  that  corresponding  to  the  height  of 
the  fall. 

Hence  it  follows  that  only  half  of  the  mechanical  momentum  of 
the  fall  comes  into  action  in  an  ordinary  under-shot  wheel,  while 
the  water  flows  off  with  half  the  velocity  with  which  it  came  on 
the  wheel ;  the  effect  of  such  a  wheel  can,  therefore,  never  exceed 
the  value  of  \  E.  Even  this  effect  cannot  be  practically  obtained, 
as  a  part  of  the  force  is  lost  by  the  adhesion  of  the  water  to  the 
walls  of  the  channel,  resistance  of  friction,  &c.  Carefully  con- 
ducted experiments  have  yielded  the  value 

e  =  0,3£ 

for  under-shot  wheels  moving  in  a  channel,  where  no  lateral  efflux 
of  the  water  could  take  place. 

But  in  unconfined  wheels,  as  those  applied  to  ship-mills,  where 
the  water  may  escape  laterally,  the  effect  is  still  more  remote  from 
the  absolute  maximum.  Under-shot  wheels  are  applied  where 
there  is  a  considerable  mass  of  water,  but  where  the  fall  is  of  small 
elevation. 

As  the  mechanical  momentum  of  the  fall  is  turned  to  little  ac- 
count in  the  above  described  under-shot  wheels,  where  the  water 
strikes  the  float-boards  at  right  angles,  Poncelet  has  constructed  an 
under-shot  wheel  with  curved  float-boards,  the  effect  of  which 
approaches  far  nearer  to  the  absolute  maximum. 

In  order  to  have  the  water  come  upon  the  wheel  without  a 
sudden  stroke,  the  float-board  at  the  circumference  of  the  wheel 


HORIZONTAL    WATER-WHEELS.  189 

must  correspond  with  the  direction  of  the  tangent ;  but  if  they 
were  so  constructed,  the  water  would  be  hindered  in  falling  from 
the  wheel ;  besides  which,  the  water  must  not  expend  all  its  velocity 
on  the  wrheel,  since  in  that  case,  it  would  have  none  left  for  flow- 
ing off.  Thus  a  certain  loss  of  power,  independently  of  the  natu- 
ral impediments,  is  unavoidable  even  in  Poncelefs  wheel. 

Wheels  writh  curved  float-boards  are  computed  to  yield  an  effect 
equal  to  two-thirds  or  even  three-fourths  of  the  absolute  maximum. 
This  result  is  explained  in  Poncelet's  wheels  by  the  water  losing 
its  velocity  as  it  ascends  the  curved  float-boards,  and  yielding  it 
almost  entirely  to  the  wheel. 

The  over-shot  Wheel  is  applied  where  there  is  a  high  fall  of  an 
inconsiderable  quantity  of  water,  as  in  small  mountain  streams. 
The  water  in  running  down  upon  it  fills  the  cells  on  one  side  of 
the  wheel,  which  is  turned  by  this  very  addition  of  weight.  Near 
the  lower  part  of  the  wheel  the  water  again  flows  out  of  the  cells. 
There  is  also  a  portion  of  the  mechanical  moment  lost  in  over-shot 
wheels,  because  the  cells  cannot  keep  the  water  down  to  the  lowest 
point  of  the  wheel,  but  begin  sooner  to  let  it  flow  out.  A  well 
constructed  over-shot  wheel  ought  to  produce  an  effect  amounting 
to  75  per  cent,  of  the  absolute  maximum,  provided  that  it  turn 
slowly,  for  in  rapid  turning  the  water  does  not  remain  in  a  hori- 
zontal position  in  the  cells,  in  consequence  of  the  centrifugal  force, 
but  rises  exteriorly,  so  that  it  falls  sooner  from  the  cells. 

The  middle-shot  wheel  is  a  kind  of  medium  between  the  over 
and  the  under-shot  wheel. 

Horizontal  Water-wheels. — Earlier  attempts  were  made  to  con- 
struct water-wheels,  but  it  is  only  recently  that  they  have  been 
practically  applied  by  Fourneyron.  The  horizontal  wheels  he 
invented  are  known  by  the  name  of  turbines. 

Fig.  159  represents  one  of  these  constructed  for  a  high  fall  of 
water. 

The  whole  mass  of  the  falling  wrater  is  collected  in  a  wide  cast 
iron  tube,  connected  with  a  cast  iron  reservoir  by  the  opening  o. 
A  hollow  tube  passes  through  the  middle  of  the  reservoir  con- 
necting the  upper  lid  with  the  bottom.  This  horizontal  bottom 
does  not,  however,  touch  the  vertical  walls  of  the  vessel,  there 
being  between  it  and  the  lateral  walls  an  annular  interval  from 
which  the  water  flows  in  a  horizontal  direction. 

This  water  thus  streaming  out  sets  the  horizontal  wheel  with  its 


190 


HORIZONTAL    WATER-WHEELS. 


vertical  spokes  in  motion ;  a  a  is  the  vertical  axis,  round  which 

the  wheel  turns,  passing 
through  the  shell  con- 
necting the  bottom  and 
the  cover  of  the  reservoir. 
To  this  axis  the  plate  b 
b  is  fastened,  opposite  to 
the  opening  of  the  reser- 
voir bearing  the  rim  of 
the  wheel  with  the  float- 
boards. 

The  float-boards  are 
curved  as  seen  in  the 
sectional  view  in  Fig. 
160  ;  in  order,  however, 
to  make  the  wrater  strike 
the  float-boards  of  the 
wheel  in  the  most  advan- 
tageous direction,  con- 
ducting curves  made  of 
tin  are  fastened  to  the 
plate  of  the  reservoir  to 
give  a  determined  direc- 
tion to  the  water. 

It  would  detain  us  too 
long  were  we  to  enter 
into  a  particular  descrip- 
tion of  the  most  advan- 
tageous curvature  for 
float-boards,  and  con- 
ducting curves.  Fourneyron^s  turbines,  if  well  constructed,  ought 
to  produce  an  effect,  amounting  to  75  p.  c.  of  the  absolute 
maximum.  Gadiat  has  simplified  them  by  leaving  out  the  con- 
ducting curves,  and  thus  lost  5  p.  c.  more  of  the  absolute  maxi- 
mus  effect,  so  that  his  turbines  yield  but  70  p.  c. 

Turbines  are  particularly  useful  for  high  falls  which  do  not 
admit  of  the  use  of  vertical  wheels. 

Attempts  have  been  made  to  enlarge  upon  the  Segner  water- 
wheel,  in  order  to  work  machinery  with  it,  but  hitherto  with  very 


HORIZONTAL    WATER-WHEELS.  191 

little  effect ;  a  very  small  motive  power  being  invariably  produced. 

The  reason  of  the  want 

Fig.  160. 

of  success  attending 
these  attempts  did  not 
arise  from  the  active 
moving  power  being 
too  small,  but  because 
the  lower  of  the  two 
pivots  around  which 
the  apparatus  turns 
has  to  bear  the  whole 
weight  of  a  large  mass 
of  water,  in  conse- 
quence of  which,  there 
is  a  disproportionally 
large  amount  of  resist- 
ance from  friction  to 
be  overcome. 

This  objection  has  been  ingeniously  set  aside  by  Jllthans  of 
Sayn,  who  has  made  such  an  alteration  in  the  apparatus,  that  the 
water  enters  the  horizontal  arms  from  below,  and  not  from  above. 
The  most  essential  part  of  the  arrangement  is  shown  in  Fig.  161. 
The  reservoir  is 

formed  by  a  cast  Fi*  16L 

iron     conducting: 

O 

pipe,  which  is 
curved  horizon- 
tally below,  and 
ends  in  a  verti- 
cally  rising  piece 
of  tube  a.  From 
the  opening  at  a, 
the  water  flows 
into  the  neck  b 
attached  to  the 

end  of  the  tube  a  in  such  a  manner  that  it  can  turn  round  it  as 
round  a  pivot.  The  water  passes  through  the  neck  b  into  the 
horizontal  arm  c,  and  flows  out  of  the  openings  at  o.  The  motion 
of  the  wheel  is  transmitted  by  the  axis  d. 


192  WATER-COLUMN    MACHINES. 

The  friction  to  be  overcome  by  such  awheel  in  revolving  round 
the  pivot  a,  must  be  very  inconsiderable,  for  the  weight  of  the 
wheel  with  all  that  is  fastened  to  it  is  almost  entirely  supported 
by  the  pressure  of  the  column  of  water,  so  that  the  pivot  a  has 
scarcely  any  pressure  to  sustain. 

In  the  apparatus  seen  at  Fig.  161,  a  large  portion  of  the  mecha- 
nical momentum  of  the  fall  must  be  lost  from  reasons  similar  to 
those  affecting  the  under-shot  wheel  with  flat  float-boards,  for  if 
the  water  imparts  all  its  velocity  to  the  wheel,  and  falls  from  the 
opening  without  any  velocity,  and  if,  therefore,  the  wheel  rotate 
with  a  rapidity  corresponding  to  the  operation  of  the  fall,  the 
pressure  backwards,  and  consequently  the  mechanical  effect  will 

be  null  also.  The  water  must  still 
retain  a  portion  of  its  velocity  of 
motion.  Much  may  be  gained  here 
by  curving  the  arms,  somewhat  in 
the  manner  represented  in  Fig.  162. 
The  water  imparts  its  velocity  gra- 
dually to  the  wheel,  flowing  through 
the  tube,  and  pressing  against  the 
curved  walls,  so  that  it  falls  at  the  opening  almost  devoid  of  all 
rapidity. 

In  Scotland  such  turbines  of  reaction  are  much  used,  on  which* 
account  they  are  often  called  Scotch  turbines. 

Water-column  Machines. — In  these  machines  the  acting  column 
of  water,  pressing  upon  a  piston  that  moves  in  a  cylinder,  imparts 
to  it  a  forward  and  backward  motion  which  is  farther  transmitted 
by  the  piston. 

Water-column  machines  are  generally  applied  for  the  purpose 
of  raising  water  to  a  considerable  height.  In  this  manner,  for 
instance,  the  salt  spring  at  Reichenhall  in  Upper  Bavaria  is  con- 
ducted by  a  circuitous  course  about  one  hundred  and  twenty  miles 
to  Rosenheim,  and  other  intermediate  places  for  the  purpose  of 
being  boiled.  On  this  road  there  are  nine  of  these  water-column 
machines,  constructed  by  Reichenbach,  to  raise  the  springs  over 
the  mountainous  heights.  Although  all  these  machines  depend 
upon  the  same  principle,  their  mode  of  action  is  in  many  respects 
different;  we  will  here  consider  with  attention  one  of  nine  of  those 
most  simply  arranged,  that  at  Nesselgrabe. 

The  pipe  Ji  leads  the  impelling  water  to  the  machine,  it  enters 


WATER-COLUMN   MACHINES. 


193 


alternately  into  the  upper  and  lower  part  of  the  cylinder  B,  where 
it  drives  the  piston  C  alternately  up  and  down. 


Fig.  163. 


17 


194  WATER-COLUMN   MACHINES. 

In  order  to  produce  this  alternation,  on  the  entrance  of  the 
water,  an  arrangement  has  been  applied  precisely  similar  to  the 
contrivance  used  for  governing  steam-engines.  Three  connected 
pistons  move  in  the  cylinder  d,  the  two  lower  ones  are  alike,  while 
the  upper  one  has  a  smaller  diameter. 

In  the  position  of  the  piston  as  represented  in  the  drawing,  the 
impelling  water  passes  through  the  pipe  e  into  the  large  cylinder, 
and  raises  the  piston  C.  The  water  above  C  flows  through  the 
pipe/* into  the  pipe  d,  and  from  thence  passes  away  through  the 
pipe  g. 

When  the  piston  C  is  raised,  the  pistons  must  be  so  displaced 
in  the  tube  d,  that  the  impelling  water  may  enter  the  large 
cylinder.  This  is  effected  by  the  pistons  descending  so  far  in  d, 
that  the  piston  i  stands  below  the  tube/",  and  the  piston  m  below 
e;  then  the  impelling  water  passes  from  the  tube  A  through  h 
andyinto  the  upper  part  of  the  cylinder  B,  drives  down  the  piston 
C,  whilst  the  water  below  C  passes  through  e  into  the  tube  d, 
flowing  off  through  the  tube  g. 

The  elevation  and  depression  of  the  pistons  in  the  tube  d  are 
effected  in  the  following  manner.  The  tube  h  is  connected  by 
the  tube  n  with  the  upper  part  of  the  tube  d:  at  the  joint  of  the 
tube  n,  a  cock  r  is  applied,  which,  according  to  its  position  at  one 
time,  connects  the  upper  part  of  the  tube  d  with  A,  and  at  another, 
cuts  off  this  connection  and  puts  the  upper  part  of  the  tube  d  in 
communication  with  the  external  air.  If,  now,  we  suppose  the 
cock  to  be  so  placed  that  the  impelling  water  can  enter  from  h  by 
means  of  this  cock  into  the  upper  part  of  d,  the  piston  s  will  be 
pressed  upon  above  and  below  by  an  equal  power  of  water;  be- 
sides this,  the  water  presses  above  on  the  piston  i,  below  on  the 
piston  m\  the  pistons,  therefore,  are  exposed  to  equal  water- 
pressure  from  above  and  below,  and  descend  by  their  own  weight. 

When  the  pistons  are  to  rise,  the  cock  r  is  so  arranged  that  the 
communication  between  h  and  the  upper  part  of  d  is  interrupted. 
Now  no  pressure  of  water  acts  upon  s,  the  water  above  s  escaping 
from  the  machine  by  the  cock.  The  water-pressure  from  above 
against  i,  is  counteracted  by  the  pressure  from  below  against  m, 
and  the  pressure  of  the  water  from  below  s,  to  which  there  is  no 
counter  pressure,  raises  the  pistons. 

The  turning  of  the  cock  is  effected  by  the  machine  itself.  At 
the  upper  end  of  the  rod  fastened  to  the  piston  C,  a  round  disc  is 


WATER-COLUMN   MACHINES.  195 

applied,  which  strikes  against  the  oblique  surface  t  on  the  rising 
of  the  piston,  and  against  the  oblique  surface  u  on  its  sinking, 
pushing  them  sideways,  and  thus  causing  a  revolution  about  the 
axis  x.  The  arm  y  is  fastened  to  this  axis,  and  the  arm  z,  by  its 
rotation,  causes  the  cock  to  turn. 

Let  us  now  further  consider  how  the  motion  of  the  piston  C  is 
transmitted  and  applied  to  the  other  parts. 

The  piston  a  is  connected  with  the  piston  C  by  means  of  a  rod 
passing  through  a  stuffing  box,  and  has  a  much  smaller  diameter 
than  C;  the  elevation  and  depression  of  the  piston  cause,  there- 
fore, a  similar  motion  in  the  piston  a ;  but  when  a  rises,  a  rare- 
faction of  air  takes  place  in  the  chamber  6,  the  lower  valve  opens, 
and  water  is  raised  through  the  suction  pipe  JVinto  the  chamber  6. 
By  the  rising  of  the  piston  a,  water  is  pressed  into  the  chamber  c, 
the  lower  valve  closes,  the  upper  one  opens,  and  the  water  is  thus 
raised  through  the  piston  into  the  reservoir  R,  and  from  this  into 
the  ascending  pipe  S. 

On  the  descent  of  the  piston,  the  valves  which  were  open,  close, 
and  vice  versa  ;  water  is  sucked  up  into  the  chamber  c,  and  raised 
from  b  into  the  reservoir,  and  the  ascending  pipe. 

If  the  diameter  of  the  piston  C  be  two,  three  or  four  times 
greater  than  that  of  the  piston  a,  we  may  raise  a  column  of  water 
(disregarding  friction  and  other  impediments)  two,  three,  or  four 
times  as  high  as  the  height  of  the  impelling  water. 

In  the  water-column  machines  we  have  been  considering,  the 
height  of  the  impelling  water  is  140  feet ;  it  raises  the  brine  to  a 
height  of  346  feet ;  but  this  column  of  salt  water  corresponds  to  a 
column  of  fresh  water  of  397  feet ;  the  diameter  of  the  piston  C 
is  20J,  that  of  the  piston  a  10  inches,  the  larger  one  having  almost 
four  times  as  great  a  diameter.  The  reason  of  the  height  of  the 
raised  column  of  water  not  being  four  times  greater  than  the 
height  of  the  impelling  water,  that  is,  not  560  feet,  is  owing  to  a 
considerable  force  being  necessary  to  overcome  friction  and  other 
resistances.  This  machine  yields,  therefore,  about  70  per  cent, 
of  the  absolute  maximum,  for  397  is  to  560  nearly  as  70  to  100. 

The  water-column  machine  at  Esang,  also  between  Reichenhall 
and  Rosenheim,  which  is  somewhat  differently  constructed,  raises 
the  spring  to  an  elevation  of  1218  feet,  equal  to  the  raising  of  a 
column  of  fresh  water  to  a  height  of  1460  feet.  The  diameter  of 


196  WATER-COLUMN   MACHINES. 

the  larger  piston  is  25  feet  8  lines,  that  of  the  smaller,  11  feet  3J 
lines. 

Great  difficulties  present  themselves  in  converting  the  back- 
ward and  forward  motion  of  the  piston,  in  these  water-column  ma- 
chines, into  a  uniformly  circular  motion,  as  seen  in  steam  engines, 
owing  to  the  water  not  being  elastic  like  steam.  But  Reichenbach 
has  ingeniously  met  this  difficulty  in  the  construction  of  a  small 
machine  at  Toscana,  by  applying  a  guiding  or  directing  piston ; 
we  cannot,  however,  here  enter  further  into  the  consideration  of 
this  subject. 


MOTION   OF   GASES. 


197 


CHAPTER    III. 


Fig.  164. 


MOTION  OF  GASES. 

IF  a  gas  be  enclosed  in  a  vessel  having  any  kind  of  opening,  it 
will  escape  through  the  opening  as  soon  as  the  gas  in  the  vessel  is 
more  strongly  compressed  than  the  air  in  the  space  communicat- 
ing with  the  aperture.  The  laws  of  the  passage  of  gases  through 
openings  in  thin  walls,  and  through  conducting  pipes,  are  analo- 
gous to  those  bodies  of  liquid  with  which  we  have  become  ac- 
quainted. The  term  gasometer  is  applied  to  an  apparatus  serving 
to  maintain  a  constant  discharge  of  gas. 

In  chemical  laboratories,  the  form  most  commonly  used  for 
gasometers  is  represented  at  Fig.  164.  A 
is  a  cylinder  of  lacquered  tin,  about  16  to 
18  inches  in  height,  and  10  to  12  inches 
in  diameter,  having  its  upper  cover 
vaulted.  On  this  cover  stands  a  second 
cylinder  5,  open  at  the  top,  resting  upon 
three  supports,  and  only  \  of  the  height  of 
the  lower  one.  The  upper  cylinder  is 
connected  with  the  lower  by  means  of  two 
tubes,  of  which  the  one  b  is  exactly  in  the 
middle  of  the  cover.  This  must  not  quite 
enter  the  lower  cylinder.  A  second  con- 
necting tube  a  reaches  almost  to  the  bot- 
tom of  the  lower  cylinder.  In  each  of  the 
tubes  there  is  a  cock,  by  means  of  which 
we  may  at  pleasure  establish  or  interrupt 
the  communication  of  the  two  cylinders.  At  e  there  is  a  short 
horizontal  tube,  which  may  also  be  closed  by  a  cock,  and  to  which 
a  screw  is  attached,  in  order  to  admit  of  other  pipes  and  openings 
being  connected  with  it.  Near  the  bottom  of  the  lower  cylinder, 
there  is  an  opening  at  d  directed  upwards,  that  may  be  closed  by 

17* 


198 


MOTION    OF    GASES. 


means  of  a  screw  or  cock.  If  we  wish  to  fill  the  lower  cylinder 
with  a  gas,  we  first  fill  it  with  water  in  the  following  manner. 
The  opening  at  d  must  be  closed,  the  three  cocks  opened,  and  then 
water  poured  into  the  upper  vessel.  The  water  flows  into  the 
lower  cylinder,  and,  as  soon  as  this  is  filled  to  e,  we  close  the  cock. 
The  remainder  of  the  air,  still  in  the  cylinder,  escapes  through  the 
tube  b.  When  the  lower  cylinder  is  thus  filled  with  water,  the 
cocks  of  the  connecting  pipes  are  closed,  and  the  screw  or  cork 
at  d  taken  off.  Water  cannot  flow  thence  because  no  bubbles 
of  air  are  able  to  enter.  But  if  we  insert  a  gas-conducting  tube 
at  d,  the  water  will  flow  out  in  its  vicinity,  whilst  bubbles  of  gas 
continually  ascend  from  it  into  the  upper  part  of  the  receiver.  In 
this  manner,  the  lower  cylinder  fills  itself  more  and  more  with  gas. 
We  may  see  how  far  the  cylinder  is  filled  with  gas  by  the  glass 
tube  f,  which  is  so  connected  above  and  below  with  the  vessel, 
that  the  water  stands  as  high  in  it  as  in  the  cylinder. 

When  the  whole  reservoir  is  filled  with  gas,  the  opening  at  d 

is  closed,  and  the  cock  of  the  connecting  tube  a  is  opened.     As 

soon  as  the  cock  e  is  opened,  the  gas  escapes  with  a  rapidity 

corresponding  to  the  pressure  of  the  column  of  water  in  the  tube  a. 

Large  gasometers  used  for  gas  illumination,  are  constructed  on 

a  different  principle: 
a  cylinder  closed  at 
the  top  dips  into  a 
large  reservoir  filled 
with  water,  (Fig. 
165).  This  cylin- 
der is  made  of  tin, 
is  ten  yards  in  dia- 
meter, contains  100 
cubic  yards  of  gas, 
and  weighs,  as  we 
will  assume,  20,000 
pounds.  It  does  not 
sink  in  the  water,  in 
consequence  of  its 

being  filled  with  gas ;  but  its  whole  weight  presses  upon  this  gas 
with  a  force  greater  than  the  pressure  of  the  atmosphere.  Accord- 
ing to  our  assumption,  this  excess  of  pressure  amounts  to  20,000 
pounds  upon  a  circular  area  of  ten  yards  in  diameter,  which  is 


Fig.  165. 


BLOWERS. 


199 


about  equal  to  the  pressure  of  a  column  of  water  of  4  inches ;  the 
water  must,  therefore,  stand  4  inches  higher  without  than  within 
the  cylinder. 

Ascending  from  below,  a  pipe  passes  into  the  cylinder,  having 
its  upper  end  open  above  the  level  of  the  water;  this  pipe  sepa- 
rates into  a  number  of  narrower  ones,  leading  to  the  mouths  of 
the  separate  gas  pipes,  from  which  the  gas  pours  out  with  a  velo- 
city corresponding  to  the  pressure  in  the  gasometer.  This  velocity 
is  constant,  because  the  gasometer,  even  though  it  sank  more 
deeply  into  the  wrater,  only  loses  a  little  of  its  weight,  as  it  is  only 
the  wall  of  the  gasometer  that  is  here  to  be  taken  into  account. 
The  pressure  upon  the  gas  is  modified  and  regulated  by  a  counter 
weight.  In  order  to  fill  the  gasometer,  the  cock  in  the  distribut- 
ing pipe  is  closed,  while  the  cock  of  another  pipe  is  opened,  con- 
necting the  interior  of  the  gasometer  with  the  apparatus  in  which 
the  gas  is  prepared. 

Blowers  or  blowing  machines,  of  various  modes  of  construction, 
are  used  in  forges.  The  most  applicable  kind,  and  that  now 
generally  used,  is  the  cylindrical  blower  as  represented  at  Fig.  166. 

Fig.  166. 


In  a  well  bored  cast  iron  cylinder  *#,  in  which  an  air-tight  piston 
c  may  be  moved  up  and  down,  the  piston-rod  a  passes  air-tight 
through  the  stuffing  box  in  the  centre  of  the  upper  cover.  The 
upper  and  lower  parts  of  the  cylinder  communicate  at  the  opening 
6  and  d,  with  the  external  air;  while  the  openings  at  g  and/ con- 


200  BLOWERS. 

vert  the  cylinder  with  a  square  box  E.  At  b  and  d  are  valves 
opening  inwards,  at  g  and/  valves  opening  outwards.  When  the 
piston  descends,  the  valve  at  d  closes,  while  that  at  f  opens,  all 
the  air  being  driven  from  the  lower  part  of  the  cylinder  into  the 
space  E.  But  in  the  meanwhile  the  valve  at  g  is  closed,  while 
the  air  presses  through  the  valve  at  b  from  without  into  the  upper 
part  of  the  cylinder.  When  the  piston  again  rises,  b  closes,  and 
all  the  air  forced  in  by  the  descent  of  the  piston,  is  carried  through 
the  opening  at  g  into  the  box  6,  while/ is  closed,  and  the  under 
part  of  the  cylinder  is  again  filled  with  air  passing  through  the 
open  valve  d.  The  air  compressed  in  E  passes  to  the  space  occu- 
pied by  the  fire  through  a  tube  applied  at  m. 

The  velocity  of  the  piston  is  greatest  when  it  passes  the  middle 
of  the  cylinder ;  it  diminishes  the  more  the  piston  approaches  the 
upper  or  lower  limit  of  its  course.  Hence  it  follows  that  the  blast 
yielded  by  such  a  cylinder  does  not  pass  out  in  a  uniform  man- 
ner at  m.  As,  however,  a  uniform  current  is  necessary  for  most 
smelting  processes,  care  must  be  taken  to  regulate  it.  This  is 
effected  either  by  applying  three  cylinders  to  the  same  air  box  E, 
whose  pistons  do  not  simultaneously  pass  the  middle  point  of  their 
course ;  or  by  suffering  the  air  to  enter  from  E  into  a  receiver, 
whose  area  is  very  large  in  proportion  to  the  volume  of  the 
cylinder.  The  larger  this  air  receiver  is,  which  is  termed  the 
regulator,  the  less  influence  will  the  irregularity  of  the  movements 
of  the  piston  exercise  upon  the  regularity  of  the  current  of  air 
passing  out  of  the  regulator. 

As  a  regulator  for  a  blower,  there  is  used  either  an  air-tight 
balloon  of  sheet  iron,  whose  contents  are  from  forty  to  fifty  times 

as  large  as  that  of  the  cylinder,  or 
else  the  water  regulator  represented 
at  Fig.  167,  which  is  quite  identical 
in  its  nature  with  the  gasometer,  as 
used  for  gas  lighting.  In  the  box 
.B,  consisting  of  iron  plates  secured 
together  so  as  not  to  admit  of  the 
entrance  of  air,  and  whose  contents  far  exceed  those  of  the  cylin- 
der, the  air  pours  through  the  tube  D  from  the  cylinder,  escaping 
through  the  tube  C.  The  air  in  the  box  B  is  enclosed  below  by 
water,  whose  level  r  r  necessarily  stands  lower  within  the  box 
than  the  surface  v  v  without. 


BLOWERS. 


201 


Fig.  168. 


On  the  difference  of  the  heights  of  the  levels  of  the  water, 
depend  the  degree  of  compression  of  the  air  at  JB,  and  the  velocity 
of  the  discharge  through  the  tube  c. 

In  order  to  determine  the  pressure  of  the  air  in  the  different 
parts  of  the  blowing  apparatus,  a  manometer  is  used,  which,  when 
applied  to  this  especial  purpose,  is  termed  a  wind-measurer.  A 
section  of  a  very  well  constructed  instrument  of  this  kind  is  repre- 
sented at  Fig.  168.  A  hermetically  closed 
block-tin  box  is  partly  filled  with  water.  A 
tube  a  passes  through  the  bottom  of  the  box, 
having  a  screw  below,  by  which  it  may  be 
secured  to  the  blower.  The  apparatus  com- 
municates by  means  of  this  tube  with  the 
upper,  part  of  the  tin  box,  where  the  air  is 
consequently  as  strongly  compressed  as  in 
that  portion  of  the  apparatus  to  which  the 
wind-measure  is  screwed.  A  graduated  glass 
tube  b  is  connected  with  the  lower  part  of  the 
tin  box.  Water  is  poured  through  an  open- 
ing in  the  cover  of  the  box,  until  the  water 
in  the  tube  stands  exactly  at  zero  of  the 
graduated  tube,  when  the  opening  is  closed 
by  a  cork  stopper.  As  soon  as  the  air  is 
compressed  in  the  upper  part  of  the  tin  box, 
the  water  rises  in  the  tube  without  any  marked 
sinking  of  the  level  of  the  water  within  the 
box ;  the  rising  of  the  column  of  water  above 
the  zero  point  of  the  glass  tube  indicates,  therefore,  the  pressure 
sustained  by  the  air  within  the  apparatus.  By  means  of  the 
cock,  the  communication  between  the  tin  box  and  the  glass  tube 
may  be  interrupted  at  pleasure. 

The  most  simple  form  of  the  bellows  is  sufficiently  well  known, 
but  with  bellows  thus  constructed,  we  are  unable  to  engender  a 
continuous  current  of  air,  such  Fi  lgg 

as  is  necessary  in  forges  and  in 
chemical  laboratories.  For  such 
purposes  compound  bellows  are 
used,  as  represented  at  Fig. 
169.  If  the  upper  division  a  of 
such  bellows  be  filled  with  air,  compressed  by  the  weight  resting 


202  LAWS    OF    THE    FLOW    OF    GASES. 

upon  the  upper  cover,  it  can  only  escape  by  the  opening  at  c,  for 
the  valve  between  a  and  b  closes  as  soon  as  the  air  becomes  more 
strongly  compressed  in  a  than  in  b.  When  the  lower  surface 
of  the  space  b  rises,  the  air  is  compressed  in  b,  raises  the  valve 
leading  to  a,  and  presses  into  the  upper  space.  On  the  descent 
of  the  lowest  side,  the  valve  between  a  and  b  closes;  the  valve 
communicating  from  b  with  the  air  opens,  b  is  again  filled  with 
air,  which  is  again  forced  into  the  upper  space.  It  will  be 
readily  understood  that  the  pouring  forth  of  air  from  a  through 
the  opening  c  is  not  interrupted  while  b  supplies  itself  with  air. 

Laws  of  the  flow  of  Gases. — The  same  laws  apply  to  the 
velocity  of  the  efflux  of  gases  that  we  have  given  for  liquids,  that 
is  to  say,  the  velocity  of  the  efflux  is 

c  =  v/  2  g  s, 

if  s  represent  the  height  of  pressure.  Here,  however,  s  is  a  mag- 
nitude not  directly  given  by  observation  as  for  liquid  bodies ;  s 
designates  the  height  of  the  column  of  fluid,  whose  pressure 
occasions  the  discharge,  and  which  is  of  the  same  nature  and 
density  as  that  flowing  out.  Gases  contained  in  a  vessel  are  not, 
however,  at  any  time  compressed  by  a  column  of  air  of  equal 
density,  and  well  defined  height,  for  even  if  the  gas  were  only 
compressed  by  the  pressure  of  the  atmosphere,  the  column  of  air 
producing  this  result  is  neither  of  uniform  density,  nor  measurable 
height.  Therefore,  even  in  this  case,  s  cannot  be  directly  obtained 
from  observation.  The  pressure  driving  the  air  from  a  reservoir 
is,  however,  usually  measured  by  the  height  of  a  column  of  water, 
or  mercury,  observed  by  means  of  a  manometer.  The  value  of 
s,  which  must  be  substituted  in  the  above  formula  for  the  velocity 
of  the  discharge,  may,  therefore,  always  be  computed  from  the 
circumstances  observed. 

[Bernouilli  gives  the  following  expression  for  the  velocity  of  an 
escaping  current  of  gas: 

v  =  ^%k(p-p') 

P 

v  =  velocity  of  the  gas;  p  =  internal,  and  p'  =  external  pres- 
sure; and  2  k  =  a  co-efficient  equal  to  155,610  for  gases  at 
32°  F.] 

The  simplest  case  that  can  be  adduced,  is  that  of  air  being 
forced  into  a  vacuum  by  atmospheric  pressure.  The  medium 
atmospheric  pressure  equipoises  a  column  of  water  32  feet  in 


LAWS   OF   THE   FLOW   OF   GASES.  203 

height,  or  10,4  metres.  But  the  density  of  the  air  having  to 
sustain  this  medium  pressure  is  770  times  less  than  that  of  water ; 
a  column  of  air,  therefore,  having  this  density  throughout,  must 
have  a  height  of  770  X  10,4  =  8,008  metres  to  counterpoise  the 
pressure  of  the  atmosphere.  For  this  case,  therefore,  s  —  8,008m, 
and  consequently  c  =  V  2  X  9,8  .  8,008  =  396ra. 

If  the  air  pour  into  a  vacuum  from  a  reservoir  in  which  it  has 
been  compressed  by  the  pressure  of  only  half  an  atmosphere,  the 
velocity  of  the  discharge  will  be  precisely  as  great  as  in  the  last 
case,  namely  396m.  The  reason  of  this  is  easily  understood,  for 
although  the  discharge  is  produced  here  by  a  pressure  of  only  half 
the  quantity  in  the  former  case,  the  air  flowing  out  has  here  only 
half  the  density.  Besides,  the  velocity  with  which  the  air  rushes 
into  a  vacuum  is  always  the  same,  whilst  the  pressure  on  which 
this  velocity  depends  may  be  very  various. 

If  the  discharge  be  directed  towards  a  space  already  containing 
air,  although  of  inconsiderable  tension,  the  tendency  to  escape  will 
necessarily  depend  upon  the  difference  of  the  two  tensions.  If 
we  designate  this  difference  by  a  column  of  air  of  the  height  H, 
and  of  the  density  of  air  more  compressed,  the  velocity  of  the 
discharge  will  be 

c  =  v/  2  g  H. 

We  will  endeavor  to  determine  the  value  of  H  in  a  case  where 
air  more  compressed  is  discharged  into  atmospheric  air  of  the 
ordinary  tension.  Let  the  compression  of  the  air  in  the  reservoir 
be  measured  by  a  column  of  water,  whose  height  we  will  desig- 
nate by  h.  This  height  h  gives  the  difference  between  the  ten- 
sion of  the  inner  and  the  outer  air,  and  we  have  only  to  determine 
what  must  be  the  height  of  a  column  of  air  of  the  density  of  the 
air  in  the  reservoir,  to  enable  it  to  counterpoise  a  column  of  water 
of  the  height  h. 

If  we  had  to  do  with  air  of  medium  atmospheric  pressure,  we 
might  substitute  a  column  of  air  of  the  height  of  770  h  for  the 
column  of  water  of  the  height  h.  In  order,  however,  to  equipoise 
the  same  column  of  water,  we  want  a  column  of  air  of  smaller 
height  if  the  air  be  denser,  the  requisite  height  bearing  an  inverse 
relation  to  the  density  of  the  air. 

Atmospheric  air  of  average  pressure,  which  is  770  times  lighter 
than  water,  is  likewise  compressed  by  a  column  of  water  of  32 
feet  or  10,4  metres,  whose  height  may  be  designated  by  6,  whilst 


204  LAWS    OF    THE    FLOW    OF    GASES. 

the  air  in  the  reservoir  has  to  sustain  the  pressure  of  a  column  of 
water  of  the  height  bf  +  h,  if  V  designate  the  height  of  a  column 
of  water  corresponding  exactly  to  the  then  height  of  the  baro- 
meter. The  density  of  air  of  average  pressure  is,  therefore,  to 
the  density  of  the  air  in  the  reservoir  as  b  :  b'  +  h  ;  the  air  in  the 

reservoir  is,  therefore,  —  -  —  times  as  dense  as  the  air  of  average 

atmospheric  pressure;  instead,  therefore,  of  a  column  of  air  of  the 
height  of  770  h  of  this  more  rarefied  air,  we  must  substitute  a 

column  of  the  height  —  —  -  —  ^—  of  this  more  rarefied  air,  and  this 
b'  +  h 

value  of  —  ~  —  '—  we  must  put  in  the  above  equation  in  the 
b'  +  h> 

place  of  H;  for  a  column  of  air  of  the  height  —  -  —  ,  and  the 

density  of  the  air  in  the  reservoir  would  entirely  counterpoise  the 
column  of  water  of  the  height  h.  The  velocity  of  the  efflux  is, 
therefore,  in  this  case 


We  should  obtain  the  quantity  discharged  in  a  second,  if  we 
multiplied  the  area  of  the  opening  by  this  value  of  c,  provided  that 
the  particles  of  air  flowed  out  in  every  part  of  the  diagonal  section 
with  equal  velocity.  The  quantity  discharged  in  t  seconds  would 
be  according  to  this 

*_,.,„„  ™» 

Experience,  however,  shows,  as  we  have  seen  in  liquid  bodies, 
that  the  actual  quantity  discharged  is  far  smaller  than  what  is 
yielded  by  theory,  and  we  must  multiply  the  theoretical  quantity 
by  a  definite  factor  ^  in  order  to  obtain  the  actual  amount. 

For  water,  this  factor  is  0,64,  and  is  almost  entirely  inde- 
pendent of  the  height  of  the  pressure,  increasing  only  very 
inconsiderably  when  the  height  of  the  pressure  diminishes.  For 
gases,  however,  the  value  of  /*  is  very  variable.  According  to 
Schmidt,  who  was  the  first  to  direct  particular  attention  to  this 
subject,  /*  is  equal  to  0,52  at  a  height  of  pressure  of  three  feet 
(water)  ;  while  d"*  Aubuissori*  s  experiments  yield  the  value  of  /*  as 
equal  to  0,65  at  heights  of  pressure,  varying  between  from  0,1  to 
0,5  of  a  foot. 


LATERAL    PRESSURE    OF    GASES.  205 

The  difference  between  the  theoretical  and  actual  quantity 
discharged,  depends  upon  causes  analogous  to  those  affecting 
liquid  bodies,  and  we  may,  therefore,  conclude  that  a  contractio 
venae,  must  occur,  although  it  does  not  admit  of  direct  obser- 
vation. 

Cylindrical  as  well  as  conical  conducting  pipes,  whether  the 
wide  opening  be  turned  inwards  or  outwards,  increase  the  quan- 
tity of  the  gas  discharged. 

Lateral  pressure  of  Gases  in  the  flowing  out.  —  When  air 
moves  through  conducting  tubes,  there  is  a  resistance  to  be 
overcome  from  friction,  for  which  a  portion  of  the  tension  of  the 
compressed  gas  must  be  employed,  and  thus  be  lost  to  the 
motion. 

The  pressure  sustained  by  the  walls  of  the  tube  from  the  ten- 
sion of  the  air  passing  through,  diminishes  in  proportion  as  it 
approaches  its  mouth,  as  we  may  see  by  applying  manometers  to 
different  parts  of  the  tube.  This  is  quite  analogous  to  the  phe- 
nomena observed  in  the  motion  of  liquids  passing  through  con- 
ducting tubes. 

The  phenomenon  of  suction  takes  place  in  the  motion  of  gases 
precisely  in  the  same  manner  as  in  the  efflux  of  liquids.  If  we 
make  an  opening  of  one  or  two  inches  in  diameter  in  the  bottom 
of  a  vessel  containing  compressed  air,  the  air  will  escape  with 
great  force.  If  we  connect  a  disc  of  wood  or  metal,  seven  or 
eight  inches  in  diameter,  with  the  opening,  it  will  not  be  pushed 
off  after  the  first  resistance  has  been  overcome  :  it  will  oscillate 
quickly,  approaching  and  retreating  from  the  opening  within  very 
short  intervals.  The  air  in  the  mean  time  will  escape  with  much 
noise  between  the  disc  and  the  wall.  On  attempting  to  remove 
the  disc,  we  must  use  as  much  force  as  if  it  were  cemented  fast 
to  the  wall. 

This  phenomenon  is  explained 
in   the   following    manner :    the 
stream  of  air  leaving  the  open- 
ing, must  spread  itself  in  a  thin 
layer  between  the  disk  and  the 
wall  (Fig.  170).    The  density  re- 
maining unchanged,  it  must  extend  in  proportion  as  it  approaches 
the  edge  of  the  disc  ;  it  finds  itself  consequently  in  the  same  case 
as  a  liquid  stream  which  is  to  fill  up  the  constantly  increasing 
18 


206  LATERAL    PRESSURE    OF    GASES. 

diagonal  section  of  a  conical  conducting  pipe.  Between  the 
disc  and  wall,  a  vacuum  is  formed,  in  consequence  of  which,  the 
atmospheric  air  pressing  from  below  against  the  disc  forces  it 
against  the  wall. 

We  may  make  this  experiment  on  a  small  scale  by  blowing  air 
with  the  mouth  through  a  tube,  at  the  end  of  which  is  a  flat 
smooth  disc.  If  we  put  a  card  while  blowing  to  the  opening  of 
the  tube  in  the  middle  of  the  disc,  we  shall  observe  the  above- 
mentioned  phenomenon. 

Faraday  has  suggested  the  most  simple  mode  of  making  this 
experiment.  On  laying  the  fingers  of  the  open  hand  closely 
together,  a  series  of  intervals  will  still  remain  from  joint  to  joint : 
whilst  the  hand  is  held  thus  horizontally,  with  the  palm  turned 
downwards,  we  must  apply  the  lips  to  the  space  intervening 
between  the  index  and  middle  finger  (near  the  roots),  and  blow 
with  as  much  force  as  possible.  If  then  a  piece  of  paper,  of  three 
or  four  square  inches,  be  applied  to  the  opening,  through  which 
this  current  of  air  passes,  it  will  neither  be  blown  away  by  this 
current,  nor  will  it  fall  by  its  weight  until  we  cease  blowing. 


ACOUSTICS. 


207 


SECTION  IV. 

ACOUSTICS. 


CHAPTER  I. 


LAWS    OF    THE    MOTION    OF    WAVES    IN     GENERAL,    AND    ESPECIALLY 
OF    WAVES    OF    SOUND. 

Vibratory  Motion. — If  a  pendulum  be  brought  out  of  its  position 
of  equilibrium,  and  then  left  to  itself,  it  will  in  the  first  place  be 
carried  back  to  a  state  of  equilibrium  by  its  gravity,  but  having 
returned  to  that  point,  it  cannot  remain  at  rest,  because  it  reaches 
it  with  a  velocity  that  drives  it  out  of  its  position  of  equilibrium ; 
and  hence  the  pendulum  makes  a  number  of  oscillations,  the  laws 
of  which  we  have  already  mentioned. 

The  mutual  position  of  the  particles 
remains  unchanged  in  the  motion  of  the 
pendulum.  If,  however,  the  relative 
position  of  the  particles  of  a  body  be 
disturbed  by  any  external  cause,  and  if 
any  forces  be  present,  tending  to  restore' 
the  original  state  of  equilibrium,  they 
will  also  take  up  an  oscillatory  motion, 
which  differs  essentially  from  the  motion 
of  the  pendulum  by  the  mutual  position 
of  the  particles  changing  every  moment ; 
we  have  here,  therefore,  to  consider  not 
only  the  oscillatory  motion  of  an  indivi- 
dual particle,  but  also  the  changes  in 
the  relative  positions  of  the  particles. 


Fig.  171. 


\ 


208  ACOUSTICS. 

The  oscillatory  movement  of  the  individual  parts  of  a  body 
may  be  of  such  a  kind  that  all  particles  simultaneously  come  into 
motion,  simultaneously  pass  the  point  of  equilibrium,  simulta- 
neously reach  the  maximum  of  their  oscillation,  and  simulta- 
neously begin  their  retrograde  motion.  Such  are  the  vibrations 
of  a  steel  bar  fastened  at  one  end,  Fig.  171,  and  of  a  cord  ex- 
tended between  two  fixed  points  (Fig. 

Fig.  172. 

172).     Such  vibrations  are    termed   by 
— '"";:.-      Weber,  "standing  vibrations." 

If  the  motions  of  the  individual  parts 

are  of  such  a  kind  that  vibratory  motion  proceeds  from  one  par- 
ticle to  another,  so  that  each  makes  the  same  oscillations  as  the 
preceding  one,  with  the  sole  exception  of  the  motion  beginning 
later,  we  have  progressive  vibrations.  By  progressive  vibrations, 
waves  are  formed.  The  motion,  the  advance  of  the  wave,  is  to  be 
regarded  as  essentially  distinct  from  the  oscillations  of  individual 
parts. 

Examples  of  wave-motion  are  afforded  by  a  quiet  surface  of 
water,  on  which  we  drop  a  stone ;  by  a  long  tense  line,  near  one 
end  of  which  we  strike  with  a  sharp  blow,  the  waves  of  sound  in 
the  air,  &c.;  we  will  consider  these  various  wave-motions  more 
particularly. 

The  vibratory  motions  may  be  greater  or  smaller,  according  to 
the  cause  of  the  disturbance  of  the  equilibrium,  and  the  nature  of 
the  force,  striving  to  restore  the  particles  to  their  former  condition 
of  equilibrium ;  so  that  the  external  form  of  the  body  may  in  con- 
sequence suffer  either  well-marked  or  inconsiderable  changes ; 
the  vibrations  may  be  slower  or  faster:  they  may  be  so  slow  as  to 
enable  us  to  follow  them  with  the  eye,  and  count  the  several 
oscillations;  while,  on  the  other  hand,  they  may  be  so  fast  as  no 
longer  to  admit  of  being  distinguished. 

If  the  vibratory  motion  of  a  body  exceed  a  certain  degree  of 
velocity,  its  combined  effect  may  produce  a  certain  impression  by 
creating  undulatory  motions  in  the  surrounding  media,  by  means 
of  which,  they  are  conveyed  to  peculiarly  adapted  organs  of  sense, 
occasioning  to  these  latter  a  characteristic  sensation. 

Thus,  vibrations  whose  rapidity  lies  within  certain  limits,  which 
we  purpose  speaking  of  more  fully,  occasion  waves  in  the  air,  or 
in  other  elastic  media,  which,  consisting  in  alternate  condensations 
and  rarefactions,  are  conveyed  to  the  ear,  and  received  by  that 
organ  as  sounds. 


WATER-WAVES.  209 

Incomparably  more  rapid  vibrations  of  the  particles  of  a  body 
conveyed  to  the  eye,  produce  the  impression  of  light,  by  means  of 
the  undulatory  motion  of  a  peculiarly  elastic  fluid,  which  we  term 
ether. 

As  the  vibrations  of  sound  as  well  as  those  of  light  are  trans- 
mitted by  undulatory  motions,  we  will  at  once  proceed  to  consider 
the  most  important  laws  connected  therewith,  beginning  with 
water  waves,  as  in  them  is  incorporated  the  idea  of  a  wave,  and 
because  a  right  comprehension  of  these  will  help  to  elucidate  other 
undulatory  motions,  as,  for  instance,  sound-waves,  which  furnish 
especially  interesting  matter  of  consideration. 

Water-waves. — If  we  throw  a  stone  into  the  water,  circular 
waves  will  be  formed,  spreading  themselves  from  a  centre  (the 
spot  where  the  stone  fell),  in  all  directions,  with  uniform  velo- 
city, when  unopposed  by  any  impediment.  The  waves  consist 
of  alternate  elevations  and  depressions  succeeding  each  other 
pretty  quickly,  and  continuing  to  spread  outward  from  the  centre. 

When  a  wave  elevation  proceeds  outward,  the  individual  par- 
ticles of  water  do  not  share  in  this  advancing  motion,  for  we  see 
when  a  piece  of  wood  swims  on  the  water,  that  it  is  alternately 
raised  and  lowered  as  the  wave  elevations  and  depressions  uni- 
formly glide  away  from  under  it. 

The  force  by  which  the  water-waves  are  propagated,  is  gravity, 
for  if,  from  any  cause,  an  elevation  or  a  depression  be  produced  on 
the  horizontal  surface  of  the  water,  the  gravity  of  the  separate 
particles  of  water  will  endeavor  to  restore  the  disturbed  horizontal 
plane,  by  which  means  an  oscillatory  motion  is  produced,  which 
by  degrees  is  propagated  from  one  particle  to  another. 

As  soon  as  regular  waves  have  been  formed,  the  separate  par- 
ticles of  water  on  the  surface  describe,  during  the  advance  of  the 
wave,  curves  returning  into  themselves,  which,  in  cases  of  extreme 
regularity,  are  circles,  while  in  cases  where  the  front  of  the  wave 
elevation  is  not  equal  to  the  succeeding  one,  the  individual  par- 
ticles of  water  describe  curves  which  are  not  closed,  but  such  as 
we  have  represented  at  Figs.  173  and  174. 

Let   us   now  consider  somewhat   more  ^J_^ 

attentively,   the    connection   between   the      (^_^/      \^? 
motion  of  the  individual  particles  of  water 
and  the  propagation  of  the  wave. 

Let  us  assume  that  a  regular  undulatory  motion,  advancing 

18* 


210 


WATER-WAVES. 


from  left  to  right,  spread  itself  to  the  particle  of  water  0  in  Fig. 
175,  obliging  it  to  describe  a  circular  course.  Now  while  the 
particle  0  completes,  for  the  first  time,  its  circular  course,  motion 
is  propagated  to  a  certain  distance.  Let  the  particle  marked  12 


Fig.  175. 


12 


15 


be  the  one  to  which  the  vibratory  motion  is  propagated  from  0, 
while  0  performs  its  revolution ;  then  will  12  begin  its  first  revo- 
lution at  the  moment  that  0  enters  upon  its  second. 

If  we  now  suppose  the  circumference  of  the  circle  described  by 
the  particle  0  to  be  divided  into  12  equal  parts,  as  well  as  the  space 
intervening  between  0  and  12,  the  undulatory  motion  in  the 
direction  from  0  towards  12  will  always  advance  one  division 
further,  whilst  the  particle  0  describes  TVth  of  its  circular  course. 

While  the  particle  0  describes  the  first  12th  part  of  its  course, 
the  undulatory  motion  extends  to  1 ;  and  while  0  is  passing  over 
the  first  quarter  of  its  course,  the  same  motion  is  transmitted 
to  3. 

Fig.  176  represents  the  moment  in  which  the  particle  0  has 

Fig.  176. 


o    i 


traversed  the  quarter  or  ^ths  of  the  circle ;  the  particle  1  has  at 
that  moment  passed  over  -&ths ;  the  particle  2  TVth ;  while  the 
particle  3  is  not  yet  displaced  from  its  position  of  equilibrium. 
Fig.  177  shows  the  moment  in  which  the  particle  0  has  traversed 


Fig.  177. 


half  its  course  ;  the  particle  1  T52~ths ;  the  particle  2  T\ ths  ;  and 
the  particle  3  f'jths  of  their  course ;  while  the  particles  4  and  5 


WATER-WAVES.  211 

are  in  the  same  position  as  the  particles  1  and  2  of  the  former 
figure.  The  particle  6,  although  not  removed  from  its  equilibrium, 
is  about  to  begin  its  motion. 

The  particle  3  has  reached  its  lowest  point;  here  is  the  centre 
of  a  wave-depression. 

If,  now,  -rath  of  the  time  necessary  for  a  particle  to  complete 
its  circuit  be  passed,  the  particle  3  will  have  come  into  such  a 
position  with  reference  to  its  original  place,  as  is  now  the  case  with 
the  particle  2;  and  the  particle  4  will  have  reached  its  lowest 
position,  being  J  of  the  circle  removed  from  its  position  of  equili- 
brium ;  the  wave-depression  has,  therefore,  advanced  from  3  to  4 
in  this  interval  of  time. 

Fig.  178  represents  the  moment  in  which  the  particle  0,  having 

Fig.  178. 


traversed  f  ths  of  its  course,  has  reached  the  highest  point  of  its 
circuit ;  here,  therefore,  is  the  summit  of  a  wave-elevation.  The 
particle  1  has  traversed  Aths;  the  particle  2  -rVhs;  and  3  -j^ths 
of  its  course ;  the  particles  4,  5,  6,  7, 8,  are  in  the  same  position 
as  1,  2,  3,  4,  and  5  of  the  former  figure.  From  the  moment  re- 
presented in  Fig.  177  to  the  moment  shown  in  Fig.  178,  the  wave- 
depression  has  moved  from  3  to  6. 

Whilst  the  particle  0  is  traversing  the  last  quarter  of  its  course, 
the  wave-elevation  advances  from  0  to  3,  and  the  depression  from 
6  to  9 ;  while,  at  the  same  moment  that  0  has  ended  its  course  for 
the  first  time,  and  is  entering  upon  a  second  circuit,  the  particle 
12  begins  its  course  for  the  first  time. 

This  moment  is  represented  in  Fig.  179,  which  needs  no  further 
explanation. 

Fig.  179. 


212  WATER-WAVES. 

Fig.  180  represents  the  moment  in  which  0  has  traversed  its 

Fig.  180. 


course  a  second  time  ;  at  this  time  12  will  have  made  its  first 
circuit ;  motion  been  transmitted  to  24,  a  wave-elevation  is  seen 
at  3,  another  at  15 ;  one  wave-depression  at  9,  and  another 
at  21. 

If  the  undulatory  motion  continue  uninterrupted,  the  individual 
particles  of  water  will  likewise  pursue  their  circuits ;  the  wave- 
elevations,  as  well  as  the  wave  depressions,  advancing  uniformly 
from  left  to  right,  while  one  particle  after  the  other  reaches  the 
highest  and  lowest  point  of  its  circuit. 

Thus  the  wave-elevations  and  depressions  advance  owing  to  the 
same  circular  motion  being  imparted  to  all  the  particles  of  water, 
each  entering  upon  that  motion  successively. 

The  distance  between  two  adjacent  particles  in  similar  con- 
ditions of  vibration,  is  called  the  length  of  a  wave;  as  the  distance 
between  0  and  12,  and  between  12  and  24,  these  particles  begin- 
ning their  oscillation  simultaneously,  and  reaching  simultaneously 
their  highest  and  lowest  points.  According  to  this,  the  distance 
from  the  summit  of  one  elevation  to  the  next,  as  from  3  to  15  in 
our  figure,  or  from  the  middle  of  one  depression  to  the  middle 
of  the  next,  as  from  9  to  21,  constitutes,  likewise,  the  length  of  a 
wave. 

Those  particles  that  are  removed  J  of  the  length  of  a  wave  from 
each  other,  as  0  and  6,  3  and  9,  9  and  15,  are  always  in  opposite 
conditions  of  vibration.  The  particle  9,  for  instance,  forms  the 
lowest  point  of  a  depression  ;  3  and  15,  on  the  contrary,  the  summit 
of  wave-elevations.  The  particles  0  and  6  are  certainly  both  in 
their  position  of  equilibrium,  but  the  motion  from  0  is  directed 
downward,  while  that  from  6  is  directed  upward. 

The  time  required  by  a  particle  to  complete  an  oscillation  is 
termed  the  time  of  an  oscillation ;  whilst  a  particle  is  completing 
an  oscillation,  the  wave  advances  a  length. 

Linear-Waves. — As  has  been  already  remarked,  the  courses  of 


LINEAR-WAVES.  213 

the  particles  of  water  are  not  always  strictly  circular,  as  we  have 
assumed  them  to  be  in  our  figures,  or  even  curves  returning  into 
themselves.  This  circular  course  is  often  converted  into  an  ellip- 
tical form;  sometimes  the  horizontal,  sometimes  the  vertical  diame- 
ter being  the  greater.  If  the  horizontal  diameter  were  null,  the 
separate  particles  would  merely  oscillate  up  and  down  at  right 
angles  to  the  direction  in  which  the  waves  are  propagated.  This 
kind  of  motion  propagates  the  waves  along  a  stretched  cord.  We 
shall,  on  a  future  occasion,  have  more  to  say  regarding  this  kind 
of  undulatory  motion  when  we  enter  upon  the  theory  of  light. 

Fig>  181.  The  lines  marked  from 

1  to  6,  in  Fig.  181,  are 
designed  to  illustrate  the 
transmission  of  such  linear 
waves.  These  lines  cor- 
respond accurately  with 
the  Figs.  176  to  180,  be- 
ing derived  from  the  lat- 
ter, on  setting  down  the 
horizontal  part  of  the  mo- 


tion as  null ;  and  they  will  not,  therefore,  require  any  further  ex- 
planation. 

If  a  linear- wave,  advancing  towards  one  fixed  point,  reach  that 
point,  it  will  be  reflected  returning  to  the  other  end,  and  will  pass 
many  times  backwards  and  forwards.  But  if  new  waves  be  con- 
tinually formed,  they  will,  in  meeting  the  reflected  waves,  form 
standing  waves,  from  the  combined  action  of  the  two  systems  of 
waves. 

We  will  not  here  pause  to  consider  any  further  the  formation  of 
standing  waves  by  the  combined  action  (interference)  of  the  direct, 
and  the  reflected  wave-system,  since  we  purpose  treating  more 
fully,  and  on  similar  principles,  of  the  formation  of  standing  air- 
waves, depending  on  the  interference  of  a  direct  and  reflected 


214  LINEAR-WAVES. 

wave  system ;  at  present,  we  will  limit  ourselves  to  the  conside- 
ration of  the  kind  of  motion  manifested  in  a  line  or  cord  during 
such  standing  vibrations. 

The  most  simple  case  is  where  the  line  vibrates  throughout  its 
whole  length  as  represented  in  Fig.  182.     This  motion  may  be 
182.  brought  about  by  removing  the 

centre  of  a  moderately  tensely 
drawn  line,  somewhat  out  of 
its  equilibrium  (which  is  best 
done  by  moving  it  somewhat 
to  the  right  or  left),  and  then 
leaving  it  to  itself.  All  the  particles  are  simultaneously  on  one 
and  on  the  other  side  of  the  position  of  equilibrium ;  they  simul- 
taneously attain  the  maximum  of  their  distance  from  the  point  of 
equilibrium  on  the  right  side,  and  simultaneously  come  to  the 
extremities  of  their  course  on  the  other  side.  The  particles,  there- 
fore, whose  points  of  equilibrium  are  /,  d,  and  g,  simultaneously 
reach  /',  df,  and  gf ;  and  simultaneously  passing  their  point  of 
equilibrium,  moving  in  the  same  direction,  they  simultaneously 
come  to/",  d",  and  g". 

While  all  the  particles  are  always,  at  the  same  time,  in  similar 
conditions  of  equilibrium,  the  amplitude  of  their  oscillations  is 
alone  different,  being  greater  for  the  particle  d  than  for/  and  g. 

The  oscillations  of  a  tense  string  disturbed  from  its  position  of 
equilibrium,  or  those  induced  by  a  bow  drawn  across  the  middle 
of  its  length,  are  of  the  same  kind.  But  the  vibrations  of  the 
string  are  so  rapid,  that  the  separate  oscillations  can  no  longer  be 
distinguished,  but,  on  the  contrary,  only  a  tone  is  produced.  We 
shall  have  once  more  further  to  consider  the  vibrations  of  the  cord 
with  reference  to  this  tone. 

The  vibrations  of  a  somewhat  loosely  strung  cord  are  slow 
enough  to  be  counted ;  it  is  difficult,  however,  to  produce  a  wholly 
regular  oscillatory  motion  in  the  manner  indicated,  if  we  bring 
the  middle  of  the  line  out  of  its  equilibrium  from  below,  since  in 
that  case  not  only  the  elasticity  of  the  line  will  bring  back  the 
particles  to  their  conditions  of  equilibrium,  but  gravity  will  also 
act ;  but  if  we  move  the  middle  of  the  line  out  of  its  equilibrium 
to  the  right  or  left,  the  motion  is  partially  that  of  the  pendulum, 
because  if  the  line  be  not  too  tightly  strung,  the  middle  always 


LINEAR-WAVES.  215 

hangs  somewhat  down ;  if,  however,  we  draw  it  tighter,  the  vibra- 
tions become  too  rapid  to  be  distinguished. 

These  regular  vibrations  in  a  string  are  best  distinguished,  if 
one  of  its  extremities  be  fastened,  while  the  other  is  held  in  the 
hand,  and  made  to  describe  small  circles  with  uniform  velocity. 
When  we  find  the  right  degree  of  rapidity  for  the  motion  of  the 
hand,  which  is  easily  done,  the  string  will  fall  into  such  motion, 
that  its  centre  will  describe  a  large  circle  around  its  point  of 
equilibrium.  All  the  other  points  of  the  line  then  turn  likewise 
in  circles  round  their  positions  of  equilibrium ;  the  circles  being 
smaller,  the  nearer  the  points  lie  to  the  extremities. 

If  we  accelerate  the  motion  of  the  hand,  the  regularity  of  the 
motion  of  the  string  will  be  disturbed  ;  it  is  easy,  however,  so  to 
accelerate  the  rapidity  of  the  motion  of  the  hand,  that  there  shall 
be  a  point  of  rest  in  the  middle  of  the  string.  Each  half  will 
vibrate  exactly  as  did  the  whole  line  in  the  former  case;  the 
middle  of  each  half  describes  larger  circles  than  the  other  points, 
and  here,  therefore,  a  belly  is  Fig.  183. 

formed.  In  Fig.  183  we  have 
represented  two  ventral  points, 
and  one  node,  for  thus  we  term 
the  resting  point  k,  separating 
the  two  vibrating  portions. 

When  /  reaches  its  highest  point,  m  attains  its  lowest  position, 
and  conversely. 

By  increased  rapidity  of  the  hand,  we  can  easily  succeed  in 
producing  two  nodes,  and  three  bellies 
as  represented  at  Fig.  184.  Fig' ] 

In  the  same  manner  the  line  may 
be  divided  into  many  parts,  always 
separated  by  a  node. 

The  nodes  may  also  be  observed  in  tense  cords.     Fig.  185 
represents  a  tense  cord  from 
which  J  of  the  length  has  Fi^185- 

been  separated  by  means  of  '^::::^Z:::::'-^^:CZl^:--';n-:C^'i:r^-J 
a  bridge,  which  so  divided 

the  cord  into  two  parts,  that  the  one  is  twice  as  long  as  the 
other.  On  touching  the  smaller  parts  with  the  bow,  the  other 
portion  will  fall  into  vibrations,  and  one  node  at «,  and  two  bellies 
at  v  and  v'  will  be  formed.  The  position  of  these  nodes  is  proved 


216  LINEAR-WAVES. 

by  little  figures  of  paper  remaining  fixed  at  these  points,  which 
fall  off  at  other  parts  of  the  cord. 

If  we  so  arrange  the  bridge,  that  the  string  is  divided  into  two 
parts,  of  which  the  one  is  only  ^th  the  length  of  the  other,  we 
shall  have  two  nodes  and  three  bellies  on  touching  the  string  with 
the  bow. 

In  metallic  plates,  bells,  &c.,  regular  vibrations  may  also  be 
produced.     In  order  to  make  plates  vibrate,  we  may  use  the  vice 
186>  shown  in  Fig.  186,  which   must  be 

firmly  fastened.  The  plate  is  placed 
between  the  cylinder  a  and  the  screw 
6,  both  of  which  terminate  in  a  piece 
of  cork  or  leather.  If  the  plate  be 
sufficiently  well  screwed  on,  we  may 
produce  vibrations  by  strokes  of  the  bow. 

We  may  thus  cause  plates  of  wood,  glass,  metal,  &c.,  to  vibrate, 
whether  they  be  triangular,  square,  round,  elliptical,  &c.  The 
vibrating  plates  produce  like  the  vibrating  cords,  tones  which  are 
sometimes  high,  and  sometimes  low.  It  is  observed  further,  that 
the  plates  may  be  separated  into  vibrating  parts,  and  lines  of 
repose  or  nodal  lines  for  each  one  of  these  tones.  In  general,  the 
extension  of  the  vibrating  parts  diminishes,  and  consequently  the 
nodal  lines  become  more  numerous  as  the  tone  rises. 

In  order  to  prove  the  existence  of  these  nodal  lines,  we  may 
strew  fine  dry  sand  on  the  upper  surface  of  the  plate,  when  the 
sand  will  rise  and  fall  during  the  tone,  and  at  last  accumulate 
upon  the  nodal  lines.  In  this  manner  arise  the  sound-figures  as 
they  were  named  by  their  discoverer  Chladni. 

A  number  of  different  figures  may  be  produced  by  means  of  the 
same  plate,  according  as  we  move  the  bow  more  or  less  violently, 
or  with  more  or  less  rapidity ;  or,  again,  according  as  we  change 
the  point  of  support  of  the  plate,  and  touch  various  parts  of  its 
edge. 

At  Figs.  187  and  188,  a  number  of  sound  figures  are  repre- 
sented as  produced  with  a  square  plate.  For  example,  in  order 
to  obtain  the  cross  whose  arms  unite  the  middle  points  of  the 
parallel  sides  of  the  square  (see  the  first  figure)  we  must  fix  the 
middle  of  the  plate,  and  move  the  bow  at  one  corner.  By  fixing 
the  middle  of  the  plate,  and  moving  the  bow  in  the  middle  of  one 


TRANSMISSION  OF  SOUND  THROUGH  THE  ATMOSPHERE.    217 
Fig.  187.  Fig.  188. 


side  of  the  square,  we  form  a  cross,  whose  arms  unite  the  oppo- 
site corners  of  the  square,  Fig.  188. 

Triangular  and  polygonal  plates  yield  similar  results. 

Transmission  of  Sound  through  the  atmosphere.— The  vibratory 
motion  of  any  body  surrounded  by  air  gives  rise  in  it  to  an  undu- 
latory  motion,  which,  on  being  transmitted  to  the  ear,  produces  the 
sensation  of  sound.  Generally  speaking,  it  is  by  means  of  the 
atmosphere  that  the  sound-waves  are  transmitted  to  our  organs  of 
hearing,  but  still  all  other  elastic  bodies,  solid  as  well  as  fluid,  are 
capable  of  conducting  sound  more  or  less  perfectly.  Sound  can- 
not, however,  be  transmitted  in  a  vacuum.  Let  us  lay  a  small 
cushion  of  wool  or  cotton  in  the  middle  of  the  plate  of  the  air- 
pump,  on  the  top  of  this  a  piece  of  clock-work  provided  with  a 
little  bell,  and  which  can  be  made  to  strike.  Over  the  whole  is 
placed  a  bell  glass,  provided  above  with  a  leather  cap,  through 
which  a  rod  passes,  by  whose  turning  the  clock-work  is  set  into 
action.  At  the  instant  the  works  begin  to  act,  the  clapper  strikes 
at  the  intervals  upon  the  bell;  no  sound,  however,  will  be  heard, 
if  the  bell  have  first  been  exhausted.  On  gradually  admitting  the 
air,  we  distinguish  the  tone  becoming  louder  and  louder  as  the 
bell  becomes  more  filled  with  air.  Sound  cannot,  therefore,  be 
propagated  through  a  vacuum. 

The  loudest  noise  on  earth  cannot,  therefore,  penetrate  beyond 
the  limits  of  our  atmosphere,  and  in  the  same  manner  not  the 
faintest  sound  can  reach  our  earth  from  any  of  the  other  planets; 
thus,  the  most  fearful  explosions  might  take  place  in  the  moon, 
without  our  hearing  anything  of  them. 

Saussure  asserts  that  the  discharge  of  a  pistol  makes  less  noise 
on  the  summit  of  Mont  Blanc,  than  the  report  of  a  small  toy 
19 


218    TRANSMISSION  OF  SOUND  THROUGH  THE  ATMOSPHERE. 

cannon  fired  off  in  the  valleys  below ;  and  Gay  Lussac  found  that 
when  he  had  risen  in  his  balloon  to  an  elevation  of  700  metres, 
(758  yds.,)  and  was  consequently  in  a  highly  rarefied  atmosphere, 
his  voice  had  lost  very  much  of  its  intensity. 

Sound  may  diffuse  itself  not  only  through  the  atmosphere,  but 
through  all  kinds  of  gases  and  vapors.     To  prove  this,  we  will 
Fi    189        hang  a  little  bell  to  an  untwisted  hemp  line  in  a 
large  balloon  (see  Fig.  189).     If  the  air  be  ex- 
hausted in  the  balloon,  we  shall  no  longer  hear  the 
sound  of  the  bell ;  as  soon,  however,  as  a  few  drops 
of  a  volatile  fluid,  as,  for  instance,  ether,  be  intro- 
duced into  the  balloon,  vapor  will  be  immediately 
formed,  and  the  tone  will  again  become  audible. 
Sound  is  readily  transmitted  in  water;  the  diver 
can  hear  what  is  said  on  the  shore,  while  persons 
on  the  shore  can  distinguish  the  noise  made  by  the  concussion  of 
two  stones  at  great  depths  below  the  surface. 

Solid  bodies  can  not  only  produce,  but  also  transmit  sound.  If 
we  apply  the  ear  to  one  extremity  of  a  beam,  20  or  30  yards  in 
length,  we  can  clearly  hear  a  slight  tap  made  at  the  other  end  of 
it,  although  the  sound  may  be  so  indistinctly  conveyed  by  the  air 
that  the  person  causing  the  noise  may  be  scarcely  conscious  of  it. 
In  order  to  comprehend  the  way  and  manner  in  which  vibra- 
tions of  sound  are  transmitted  through  the  atmosphere,  we  will 
suppose  the  air  at  one  end  of  an  open  tube  to  be  put  into  a  con- 
dition of  oscillation  by  the  vibratory  motion  of  a  piston 
applied  at  the  other  extremity. 

Fig.  190  represents  such  a  tube;  the  lines  drawn  at 
equal  distances  designate  strata  of  air  of  equal  density; 
p  is  the  piston  which  moves  rapidly  backwards  and 
forwards  along  the  distance  a  g,  Fig.  191. 


Fig.  191. 


Fig.  190. 


Fig.  192. 


Fig.  193. 


3  6 


9  12  15  18  21 


369  12  15  16  21  24 


TRANSMISSION  OF  SOUND  THROUGH  THE  ATMOSPHERE.   219 

I 

Fig.  194. 

HM  _     >  ^ MI 

3  6      9       12  15  18  21  24 

Such  an  oscillating  motion  cannot,  as  we  have  already  said,  be 
uniform.  Let  us  suppose  the  time  necessary  for  the  piston  to 
move  backwards  and  forwards,  that  is,  from  a  to  g,  and  again  from 
g  back  to  a,  to  be  divided  into  twelve  equal  parts  ;  it  will  traverse 
in  the  first  of  these  periods  the  distance  a  b,  in  the  second  the  dis- 
tance b  c,  in  the  third  c  </,  &c. ;  the  motion  which  was  at  first 
slow,  increases,  therefore,  in  rapidity,  which  at  the  end  of  the  third 
period  of  time,  is  at  its  maximum ;  at  the  sixth  division  of  time  it 
is  at  0,  when  the  piston  reaches  the  right  extremity  of  its  course, 
and  then  begins  its  retrograde  motion. 

We  obtain  the  points  b  c  d,  &c.,  by  drawing  a  circle,  whose 
diameter  a  g  is  equal  to  the  amplitude  of  the  oscillation,  dividing 
the  circumference  of  this  circle  into  twelve  equal  parts,  and  letting 
fall  perpendiculars  from  these  points  upon  a  g. 

Now  this  motion  of  the  piston  is  transmitted  by  degrees  to  all 
the  separate  layers  of  air  of  the  tube,  each  of  which  will,  after  a 
time,  make  the  same  oscillations  as  the  piston ;  the  motion  begin- 
ning later  in  proportion  as  each  layer  is  further  removed  from  the 
piston. 

If  the  air  were  perfectly  unelastic  and  rigid,  the  whole  column 
of  air  in  the  tube  would  be  pushed  out  by  the  motion  of  the 
piston,  all  the  separate  layers  of  air  acquiring  simultaneously  the 
motion  of  the  piston ;  but  air  is  elastic,  and  motion  is  only  gradu- 
ally propagated  by  the  layers  nearest  the  piston  being  first  com- 
pressed, and  then  by  their  elasticity  acting  upon  the  succeeding 
ones. 

If  we  .consider  the  condition  of  the  air  at  the  moment  at  which 
the  piston,  after  the  beginning  of  its  motion,  has  traversed  half  its 
course  towards  the  right,  being  consequently  removed  the  distance 
a  d,  as  represented  in  Fig.  192,  from  its  original  position,  we 
shall  see  that  motion  has  only  been  transmitted  to  the  layer  of  air, 
marked  3 ;  that  is  to  say,  the  layer  of  air  3  is  still  in  its  original 
position ;  the  air  between  it  and  the  piston  being  compressed,  this 
layer  3  is  also  urged  forward,  and  thus  begins  its  motion. 

The  layers  of  air  1  and  2  (not  marked  in  the  figure,  because 
from  their  position  there  can  be  no  doubt  which  are  intended), 
have  begun  their  motion  subsequently  to  that  of  the  piston,  and 


220    TRANSMISSION  OF  SOUND  THROUGH  THE  ATMOSPHERE. 

are  therefore  not  so  far  removed  from  their  original  position.  The 
layer  1  began  its  motion  later  by  V^th  of  time  necessary  for  the 
piston  to  pass  backwards  and  forwards;  the  layer  2,  T\ths  later; 
1  has,  therefore,  been  moved  the  distance  a  c  from  its  original 
position,  and  2  only  the  distance  a  b. 

In  this  manner,  the  mutual  position  of  the  layers  of  air  between 
3  and  the  piston,  may  be  ascertained  as  exhibited  in  Fig.  192. 

Fig.  193  shows  the  piston  at  the  moment  in  which  it  has 
reached  the  right  end  of  its  course,  and  consequently  is  removed 
the  distance  a  g  from  its  original  position.  Motion  has,  in  the 
mean  time,  been  transmitted  to  the  layer  of  air  6,  which  then 
begins  to  move. 

The  piston  has  just  come  to  rest,  and  is  about  to  begin  its  retro- 
grade motion;  3  has,  however,  just  attained  the  greatest  velocity 
in  its  motion  from  left  to  right. 

The  layers  of  air  are  removed  from  their  original  position  as 
represented  in  Fig.  190,  to  the  distances  represented  in  the  accom- 
panying table. 

The  layer  1  is  removed  to  the  distance  af 
it  2  "  "  "  "  a  e 
"  3  "  "  "  "  a  d 
"  4  "  "  "  ii  a  c 
"  5  "  "  "  «  a  b 

tt          Q  tt  tt  tt  tt       Q 

Fig.  193  represents  the  position  above  indicated  of  the  various 
layers.  The  greatest  condensation  of  the  air  occurs  at  3. 

While  the  piston  now  returns  from  its  position  at  Fig.  193  to  its 
original  situation,  motion  is  propagated  to  the  layer  12 ;  this  layer 
of  air  begins  its  motion  for  the  first  time,  at  the  same  moment  in 
which  the  piston  begins  a  second  time  to  move  towards  the  right. 
This  position  of  the  separate  layers  of  air  between  12  and  the 
piston,  as  represented  at  Fig.  194,  takes  place  by  the  following 
consideration. 

While  the  piston  and  the  layer  of  air  12  assume  their  original 
position,  and  are  momentarily  at  rest,  all  the  intermediate  layers 
of  air  are  removed  from  their  original  positions ;  all  the  layers  of 
air  between  the  piston  and  6  have  a  retrograde  motion  from  right 
to  left,  while  those  between  6  and  12  go  from  left  to  right.  The 
layers  of  air  are  removed  from  their  original  positions,  as  indicated 
in  the.  following  table. 


TRANSMISSION  OF  SOUND  THROUGH  THE  ATMOSPHERE.   221 

The  layer  1  is  removed  the  length  a  b 
"2  "  "         a  c 

"3  "  "          ad 

"      4  "  "          a  e 

"      .5  "  "          af 

"      6  "  "          ag 

"      7  "  "          af 

"      8  "  "         a  e 

"9  "  "          a  d 

«    10  «  «          a  c 

"     11  "  "          a  b 

"    12  "  "          0 

We  see  here,  that  at  9  there  is  the  greatest  condensation,  and  at 
3  the  greatest  rarefaction  ;  the  layer  3  has  just  attained  its  greatest 
velocity  towards  the  left,  and  the  layer  9  towards  the  right. 

If,  now,  the  piston  remain  at  rest,  the  layers  1,  2,  3,  4,  &c., 
will  successively  return  to  their  original  positions,  remaining  at  rest 
while  motion  is  transmitted  towards  the  right ;  at  the  moment,  for 
instance,  in  which  3  recovers  its  original  position,  motion  will  be 
transmitted  to  15;  the  maximum  of  condensation  will  be  at  12, 
and  the  maximum  of  rarefaction  at  6 ;  at  the  moment  in  which 
12  recovers  its  original  position,  the  maximum  of  condensation 
has  advanced  to  15,  and  the  maximum  of  rarefaction  to  21,  when 
the  layer  24  begins  its  first  motion. 

From  the  piston  to  12  there  is  one  wave,  from  12  to  24  a  second ; 
for  the  length  of  a  wave  is  the  distance  between  two  particles  in 
similar  conditions  of  oscillation  ;  the  piston  and  the  layers  12  and 
24  begin  their  motion  simultaneously  to  the  right;  they  traverse 
their  course  in  the  same  direction,  returning  in  like  time  and 
manner. 

Each  wave  consists  of  a  rarefied  and  a  condensed  part ;  the 
former  corresponding  to  the  wave  depression,  the  latter  to  the 
wave  elevation  of  water-waves. 

The  distance  from  one  point  of  the  maximum  of  density  to  the 
next,  that  is,  from  9  to  21,  and  likewise  the  distance  from  one  point 
of  the  maximum  of  rarefaction  to  another,  consequently  from  3  to 
15,  is  also  the  length  of  a  wave. 

Fig.  195  represents  the  moment  in  which  the  piston,  having  com- 
pleted its  oscillation  for  the  third  time,  has  created  three  perfect  and 
successively  advancing  waves.  The  layers  that  move  in  the  same 

19* 


222    TRANSMISSION  OF  SOUND  THROUGH  THE  ATMOSPHERE. 

Fig.  195.  direction  are  indicated  in  the  figure  by  being  joined  toge- 
ther by  brackets.  The  middle  one  of  these  divisions  always 
corresponds  to  a  maximum  of  condensation  or  rarefac- 
tion, the  layers  of  air  being  at  the  highest  point  of  their 
speed,  either  to  the  right  or  left.  The  layers  of  air 
occurring  at  the  points  of  contact  of  two  brackets  are 
momentarily  at  rest,  being  either  at  the  right  or  left 
extremity  of  the  course,  which  they  traverse  during  their 
vibrations. 

Since,  as  we  shall  presently  see,  the  speed  with  which 
sound-waves  are  transmitted,  is  independent  of  the  time 
during  which  each  individual  particle  makes  a  complete 
oscillation,  and  since  the  wave-length  is  the  distance 
which  a  wave  advances  whilst  a  single  layer  of  air  is 
completing  a  perfect  oscillation,  it  is  clear  that  the 
wave-length  increases  in  the  same  proportion  as  the 
time  of  oscillation  for  the  separate  layers  of  air.  If  the 
piston,  and  consequently  the  succeeding  layer  of  air, 
require  double,  triple,  and  quadruple  the  time  to  make 
one  oscillation,  that  is,  one  backward  and  forward  mo- 
tion, the  wave-length  would  become  twice,  thrice,  or 
fourfold  as  great. 

We  have  here,  for  the  sake  of  simplicity,  considered 
the  propagation  of  air-waves  in  a  tube ;  waves  in  free 
air  are,  however,  transmitted  in  the  same  manner  from 
oscillating  bodies  in  all  directions ;  as  circular  waves 
are  formed  around  the  spot  in  the  water  in  which  the 
stone  has  fallen,  so  also  do  spherical  air-waves  arise 
round  the  oscillating  body. 

We  have  now  seen  the  manner  in  which  sound  (mean- 
ing thereby  all  action  on  the  organs  of  hearing)  arises  and  is  propa- 
gated ;  the  impressions  produced  upon  our  hearing  are,  however, 
very  various  in  their  nature.  The  sound  heard  from  a  sudden  and 
single  blow,  as  from  an  explosion,  or  any  other  cause  producing 
strong  condensation  of  the  air,  and  then  advancing  in  the  manner 
already  considered  without  being  succeeded  by  further  waves,  is 
termed  a  report;  a  sound,  on  the  contrary,  arising  from  regular 
oscillations,  and  propagated  by  regularly  succeeding  equal  waves, 
is  called  a  tone.  If  the  undulatory  motion  transmitted  by  the  sound 


VELOCITY    OF    SOUND.  223 

to  the  ear  become  more  and  more  irregular,  the  £pne  is  converted 
into  noise. 

There  are  great  differences  between  tones,  the  greatest  being 
that  manifested  between  high  and  low  tones.  The  height  of  the 
tone  is  proportional  to  the  shortness  of  the  times  of  oscillation  of 
the  body  producing  it,  and  to  the  shortness  of  the  air-wave  pro- 
pagating it. 

The  intensity  of  the  tone  does  not  depend  upon  the  times  of  the 
oscillations,  or  the  wave-length,  but  upon  the  amplitude  of  the 
oscillations ;  the  greater  the  latter  is  in  the  sounding  body,  the 
more  considerable  is  the  amount  of  condensation  and  the  succeed- 
ing rarefaction  of  the  air-waves  transmitting  the  tone. 

The  sound  or  quality  of  the  tone  is  far  more  difficult  to  define 
than  its  intensity ;  at  an  equal  elevation  of  tone,  the  character  of 
the  tones  produced  from  a  violin  are  very  different  from  those  of  a 
flute ;  natural  philosophers  are  not  agreed  as  to  the  cause  of  this 
difference,  but  it  is  probable  that  it  depends  upon  the  order  in 
which  the  velocities  and  the  changes  of  density  succeed  each 
other  in  the  different  layers  of  air  intervening  between  the  two  ends 
of  the  waves ;  and  that,  in  many  cases,  the  condensed  and  rarefied 
parts  of  the  same  may  be  unsymmetrical. 

Velocity  of  Sound. — Ml  tones,  whatever  be  their  height  or  depth, 
their  intensity  or  quality,  are  propagated  through  the  atmosphere 
with  equal  velocity,  for  if  different  persons  listen  to  a  concert  from 
different  distances,  they  hear  exactly  the  same  measure  and  har- 
mony, which  would  be  impossible  if  the  higher  tones  advanced 
with  greater  or  less  rapidity  than  the  lower  tones. 

While  light  is  propagated  with  a  velocity  that  cannot  be  com- 
puted by  human  measurement,  sound  requires  a  given  time  to 
advance  to  any  distance,  and  hence  we  are  enabled  to  explain 
several  phenomena  which  we  have  often  occasion  to  observe. 
If,  for  instance,  we  watch  from  some  distance  a  stonemason  at 
work,  we  do  not  hear  the  sound  of  the  blow  at  the  moment  in 
which  we  see  the  hammer  strike,  but  only  after  it  has  been  raised, 
as  if  the  sound  were  produced  by  the  removal  of  the  hammer  from 
the  stone,  and  not  by  its  contact  with  it.  On  seeing  a  regiment 
march  to  the  measure  beaten  on  the  drums  preceding  them,  we 
observe  an  undulatory  motion  transmitted  from  the  drummers 
through  the  whole  rank,  which  is  explained  by  the  fact  that  all  the 


224  ON  THE  REFLECTION  OF  SOUND. 

men  do  not  advance  simultaneously,  owing  to  the  hindmost  hearing 
the  beats  of  the  cfrum  later  than  the  foremost. 

The  rapidity  of  sound  may  be  ascertained  by  the  very  simple 
means  of  noting  the  time  that  intervenes  between  the  flash  and  the 
report  of  a  cannon  discharged  at  a  known  distance  from  the 
observer.  This  observation  admits  naturally  of  being  most  readily 
carried  out  at  night.  Several  very  exact  experiments  of  this 
nature  were  made  by  a  party  of  scientific  men,  at  Paris,  in  1822. 
The  distance  between  the  cannon  and  the  observer  was  9549,6 
toises  (1  toise  =  6  Paris  feet),  and  54,6  seconds  intervened  be- 
tween the  flash  and  the  report ;  whence  it  follows,  that  sound 
travels  in  an  ordinary  state  of  the  atmosphere  174,9  toises  = 
1049,4,  or,  in  round  numbers,  1050  feet  =  340,88  metres  in  a 
second. 

[Sir  John  Herschel  has  shown  that  sounds  travel  at  a  tempera- 
ture of  62°  F.  at  the  rate  of  1125  feet  per  second,  or  12f  miles 
per  minute,  or  765  miles  an  hour.  Thus,  if  a  flash  of  lightning 
is  seen  12  seconds  before  the  thunder  is  heard,  the  explosion  took 
place  at  a  distance  of  4500  yards.  I"  :  1125  ::  12''  :  13500 
ft.  =4500  yards.] 

Through  other  media  the  rapidity  of  the  propagation  of  sound  is 
not  the  same ;  being  transmitted  through  iron  16f ,  and  through 
water  4J  times  faster  than  through  the  air. 

On  the  reflection  of  Sound,  and  on  the  Echo. — On  passing  from 
one  medium  to  another,  sound-waves  always  experience  a  partial 
reflection;  while  on  coming  in  contact  with  a  solid  impediment, 
they  are  almost  entirely  reflected. 

Whether  the  reflection  be  partial  or  entire,  the  angle  of  reflec- 
tion is  always  equal  to  the  angle  of  incidence. 
Let  s  sf,  Fig  196,  be  the  separating  surface  of 
the  two  media,  say  air  and  water,  and  suppose 
!  a  sound-wave  move  in  the  direction  d  i  against 
the  surface  of  the  water,  one  portion  of  the 
motion  will  pass  over  to  the  water,  while  another  will  be  trans- 
mitted in  the  direction  i  r,  which  makes  as  great  an  angle  with 
the  perpendicular  i  p  as  d  i]  that  is  to  say,  the  angle  of  reflection 
r  i  p  is  equal  to  the  angle  of  incidence  dip.  The  same  pheno 
menon  would  occur,  according  to  the  same  law,  if  s  s'  were  the 
separating  surface  of  two  gases,  or  merely  of  two  layers  of  gas  ot 
different  density,  or  if  s  s'  were  the  bounding  surface  of  a  solid 


ON   THE    REFLECTION    OF    SOUND.  225 

body,  excepting  that  in  the  latter  case  the  reflected  tone  would  be 
far  more  intense.  An  observer,  therefore,  standing  at  any  point 
of  the  line  i  r,  would  hear  the  sound  as  if  issued  from  i,  or  from 
a  point  in  the  prolongation  of  the  line  r  i.  On  this  general  prin- 
ciple rests  the  explanation  of  an  echo. 

If  the  echo  send  the  tone  back  to  its  starting  point,  the  sound- 
waves strike  the  reflecting  surface  at  right  angles.  In  this  case, 
an  echo  may  repeat  a  larger  or  smaller  number  of  syllables 
under  conditions  that  may  be  easily  ascertained.  If  we  speak 
fast,  8  syllables  may  distinctly  be  uttered  in  2  seconds,  but  in 
that  period  of  time  sound  traverses  twice  350  yards ;  if,  there- 
fore, an  echo  be  at  a  distance  of  350  yards,  all  the  syllables 
will  be  given  back  in  their  proper  order,  the  first  coming  to  the 
speaker  in  2",  that  is,  when  he  has  given  utterance  to  the  last 
syllable.  At  this  distance,  an  echo  may,  therefore,  repeat  7  or  8 
syllables ;  there  are,  however,  echoes  capable  of  giving  back  14 
or  15  syllables. 

The  reflecting  surface  need  not  be  hard  and  flat,  as  we  often 
observe  at  sea,  that  clouds  form  an  echo. 

Sound-waves  must  also  be  reflected  in  a  cloudless  atmosphere, 
when  the  sun  develops  heat  with  its  full  force  on  the  earth's  sur- 
face, since  the  radiation  of  heat  cannot  be  equal  in  all  parts, 
owing  to  dampness,  shade,  and  other  causes.  This  unequal 
temperature  occasions  a  number  of  warm  ascending  and  cold  de- 
scending currents  of  air,  of  unequal  density ;  as  often,  therefore, 
as  a  sound-wave  passes  from  one  current  of  air  to  another,  it  will 
experience  a  partial  reflection ;  and  if  this  be  not  strong  enough 
to  occasion  an  echo,  it  will  at  any  rate  materially  weaken  the 
direct  tone.  This  is  evidently  the  reason,  as  Humboldt  observes, 
that  sound  is  propagated  further  by  night  than  by  day,  even  in 
the  midst  of  the  woods  of  America,  where  the  many  animals  silent 
in  the  day  fill  the  atmosphere  during  the  night  with  a  thousand 
confused  noises. 

The  explanation  of  multiple  echoes,  that  is,  such  as  give  back 
the  sound  many  times,  rests  upon  the  same  principles;  for  as  one 
reflected  tone  can  be  returned  anew,  it  is  evident  that  two  re- 
flecting surfaces  may  mutually  reflect  a  tone,  as  two  opposite 
mirrors  reciprocally  reflect  light.  Thus,  an  echo  of  this  sort  may 
arise  between  two  distant  parallel  walls.  There  was  formerly  an 


226 


ON   THE   REFLECTION   OF   SOUND. 


Fig.  197. 


echo  of  this  kind  at  Verdun,  occasioned  by  two  contiguous  towers, 
which  repeated  the  same  word  12  or  13  times. 

There  are  likewise  echoes  which  bear  a  tone  to  a  definite  spot. 

Let  us  assume  that  the  diagonal 
section  of  an  arch  is  an  ellipse, 
see  Fig.  197,  whose  foci  are  f 
and  f1.  A  tone  issuing  from  f 
will  be  reflected  from  all  parts 
of  the  arch  tof,  it  being  a  pro- 
perty of  an  ellipse,  that,  if  we 
draw  lines  from  f  and  f  to  the  same  point  of  the  curve,  they 
will  form  equal  angles  with  the  normal  of  this  point.  If,  there- 
fore, one  person  stand  at  f^  and  another  at  f1,  they  will  be  able 
to  understand  each  pther,  although  they  may  speak  in  a  low 
voice,  and  the  distance  of  the  two  points  f  and  ff,  amount  to 
from  50  to  100  feet,  while  not  a  word  can  be  heard  at  the  inter- 
vening points. 

The  actions  of  the  speaking-trumpet  and  the  hearing-trumpet 
may  also  be  explained  on  the  principle  of  the  reflection  of  sound. 


LAWS   OF   THE   VIBRATIONS    OF   MUSICAL   TONES.        227 


CHAPTER  II. 

LAWS  OF  THE  VIBRATIONS  OF  MUSICAL  TONES. 

Formation  of  regular  Mr-waves  in  covered  pipes. — If  a  sound- 
wave enter  the  open  end  of  a  tube  closed  at  the  opposite  extremity, 
it  will  be  reflected  on  the  surface  of  the  tube,  but  the  reflected 
waves  meeting  the  newly  entered  waves,  will  form  standing  air- 
waves by  the  combined  action  of  both  wave  systems,  provided  the 
length  of  the  pipe  bear  a  proper  proportion  to  the  length  of  the 
sound-wave. 

If  we  assume  the  length  of  the  tube  R  S,  Fig.  198,  to  be  Jth  of 

Fig.  198. 


the  length  of  the  sound-wave  entering  it,  then  the  distance  from 
the  opening  to  the  bottom,  and  back  from  the  bottom  to  the 
opening,  is  exactly  J  a  wave-length ;  the  waves  of  incidence  and 
reflection,  which  meet  at  the  opening  of  the  tube,  are,  therefore, 
removed  from  each  other  half  a  wave-length  in  their  course  ;  the 
maximum  of  the  density  of  the  wave  of  incidence  coinciding, 
therefore,  with  the  maximum  of  the  rarefaction  of  the  wave  of 
reflection,  and  conversely,  at  the  opening  of  the  tube,  there  is, 
therefore,  neither  condensation  nor  rarefaction. 

Let  us  now  consider  the  condition  of  motion  of  the  layer  of  air 
filling,  in  a  state  of  equilibrium,  the  opening  of  the  tube. 

We  have  already  seen,  in  Fig.  194,  that  if  there  be  a  maximum 
of  density  in  a  definite  spot,  as  at  9,  the  particle  6,  whose  position 
of  rest  lies  one-fourth  of  the  wave-length  from  the  point  of  rest  of 
the  particle  9,  will  be  moved  to  the  furthest  point  from  its  position 
of  equilibrium  in  the  direction  of  the  advancing  wave,  whilst  the 
particle  12,  whose  position  of  equilibrium  lies  one-fourth  of  a  wave- 


228        LAWS    OF    THE   VIBRATIONS    OF    MUSICAL    TONES. 


length  further  on  than  the  position  of  equilibrium  of  9,  will  assume 
at  this  moment  a  state  of  equilibrium. 

At  the  moment,  therefore,  in  which  the  maximum  of  density  of 
the  incident  wave  meets  the  bottom  of  the  tube,  the  layer  of  air  at 
the  opening  has  been  moved  to  its  maximum  advancement  toward 
the  right,  by  means  of  this  incident- wave,  while,  at  the  same 
moment,  it  is  not  driven  to  the  opposite  side  by  the  reflected  wave ; 
thus  it  appears,  that,  at  the  instant  in  which  the  wave  of  incidence 
arrives  at  the  bottom  of  the  tube  with  the  maximum  of  rarefaction, 
the  layer  of  air  at  the  entrance  has  experienced  its  furthest  removal 
to  the  left  from  its  position  of  equilibrium,  by  the  influence  of  the 
reflected  wave ;  the  layer  of  air  at  the  entrance  of  the  tube  vibrates, 
therefore,  alternately  from  right  to  left,  that  is,  towards  and  from 
the  bottom,  without,  however,  any  condensation  or  rarefaction  oc- 
curring. 

All  the  remaining  layers  of  air  in  the  tube  have  now  simulta- 
neously a  similar  motion,  the  extent  of  the  vibrations  being  small 
in  proportion  as  they  lie  near  the  bottom.  This  is  illustrated  in 
Figs.  199,  200  and  201.  Fig.  199  represents  the  separate  layers 

Fig.  199. 


Fig.  200. 


J 


Fig.  201. 


I  I  I  I  I  M  HIM  I  I  I  I  I  I  I  I  I  I  I  I 

of  air  in  the  tube  in  their  positions  of  equilibrium  ;  from  this  posi- 
tion of  equilibrium  they  move  simultaneously  towards  the  right, 
reaching  the  position  of  Fig.  200  after  one-fourth  of  an  undulation. 
In  this  position  of  the  layers,  the  air  is  naturally  strongly  con- 
densed at  the  bottom  of  the  tube.  All  the  particles  then  move 
simultaneously  from  the  bottom,  simultaneously  passing  the  posi- 
tion of  equilibrium,  and  simultaneously  reaching  the  position  indi- 
cated at  Fig.  201.  At  this  moment,  a  rarefaction  takes  place  at 
the  bottom  of  the  tube. 


LAWS    OF    THE   VIBRATIONS    OF   MUSICAL    TONES.        229 

Our  drawing  has  been,  for  the  sake  of  clear  illustration,  exces- 
sively exaggerated,  at  least  as  far  as  relates  to  the  amplitude  of 
oscillation  as  occurring  in  a  pipe  of  the  length  represented,  for  the 
layer  of  air  in  a  state  of  equilibrium  at  the  entrance  of  the  pipe, 
would  not  enter  so  far  into  it,  or  pass  so  far  out  of  it,  but  merely 
oscillate  a  little  to  the  right  and  left  during  the  vibrations.  If, 
however,  the  amplitude  of  oscillation  had  not  been  taken  on  so 
large  a  scale,  it  would  have  been  difficult  to  indicate  clearly  the 
difference  between  the  condensation  and  rarefaction. 

Here,  therefore,  a  regular  wave  has  also  been  formed  by  the 
interference  of  the  direct  and  reflected  waves,  for  all  the  separate 
layers  of  air  in  the  tube  begin  their  motion  simultaneously,  simul- 
taneously reaching  the  limits  of  their  course,  and  then  beginning 
their  motion  in  opposite  directions. 

Figs.  202,  203,  204,  are  intended  to  illustrate  the  rarefactions 
and  condensations  alternately  produced  in  such  regular  air-waves. 

Fig.  202. 


Fig.  203. 


Fig.  204. 


In  Fig.  202,  the  whole  tube  is  uniformly  shaded,  and  corresponds 
to  the  case  where  the  air  is  of  uniform  density  throughout  the 
whole  tube,  as  it  is  in  the  moments  at  which  all  the  individual 
layers  of  air  pass  their  position  of  equilibrium  with  their  maximum 
speed.  If  the  particles  have  come  to  the  extreme  points  of  their 
course  in  their  oscillation  towards  the  closed  end  of  the  tube,  a 
condensation  takes  place  as  seen  in  Fig.  203. 

Now  the  separate  layers  of  air  begin  to  move  away  from  the 
20 


230        LAWS    OF    THE   VIBRATIONS    OF    MUSICAL    TONES. 

closed  end,  and  after  half  an  undulation,  we  have  a  rarefaction, 
as  in  Fig.  204. 

At  the  open  end  of  the  tube,  there  is  at  no  moment  of  time  any 
marked  condensation  or  rarefaction,  the  layers  of  air  moving 
backwards  and  forwards  between  the  furthest  limits.  The  arrows 
in  Figs.  203  and  204  indicate  the  direction  in  which  the  particles 
begin  to  move,  when  the  condensation  or  rarefaction  has  just 
reached  its  maximum  at  the  bottom. 

If,  now,  a  hole  be  made  in  the  tube  at  r,  for  instance,  it  will 
hinder  the  formation  of  the  regular  wave,  because  the  air  will 
escape  thence  at  the  moment  of  condensation,  and  flow  in  again 
at  the  moment  of  rarefaction.  But  the  disturbing  influence  of 
such  an  opening  would  be  less  considerable  at  the  places  nearest 
the  open  extremity,  since  rarefaction  as  well  as  condensation 
would  be  less  at  such  points. 

Cutting  away  the  tube  at  these  parts  would  produce  the  same 
disturbing  effect  as  an  aperture. 

The  formation  of  a  regular  air-wave  in  the  tube  is,  therefore, 
dependent  upon  certain  relations  existing  between  the  length  of 
the  tube  and  the  wave-length  of  the  incident  tone  ;  in  the  case 
we  have  considered,  the  length  of  the  tube  was  one-fourth  of 
the  wave-length  of  the  incident  tone ;  standing  air-waves  may, 
however,  be  found  in  the  tube  under  other  relations  than  those 
we  have  considered  between  the  tubes  and  the  wave-length. 

It  is  essential  to  the  formation  of  regular  waves  in  the  tube, 
that  the  amplitudes  of  oscillation  should  become  so  small  as 
almost  to  disappear  close  to  the  bottom,  but  that  an  alternate 
state  of  rarefaction  and  condensation  should  take  place,  while  no 
such  apparent  changes  are  going  on  at  the  entrance  of  the  tube, 
since  there  the  condensed  part  of  the  reflected  wrave  must  always 
coincide  with  the  rarefied  portion  of  the  incident  wave,  and 
inversely. 

This  condition  is  certainly  complied  with  in  making  the  open- 
ing of  the  tube  \  of  a  wave-length  from  the  bottom ;  the  same, 
however,  is  effected  by  letting  the  distance  between  the  entrance 
and  bottom  of  the  tube  amount  to  fth,  fth,  Jth,  &c.,  of  the  wave- 
length. 

In  Fig.  205,  the  line  a  b  represents  the  length  of  the  tube 
amounting  to  }ths  of  a  wave-length;  if,  then,  b  c  =  c  d  =  d  a  = 


LAWS    OF   THE   VIBRATIONS    OF   MUSICAL    TONES.        231 

J  b  a  =  Jth  of  the  wave-length,  the  rarefied  portion  of  the  wave 
will  be  at  c,  as  the  wave  system  advances  from  a  to  b, 
while  the  condensed  part  will  be  at  a,  because  c  and  a 
are  removed  \  a  wave-length  from  each  other.     If  the    -f- 
wave  system  were  to  extend  beyond  Z>,  a  condensation 
would  again  occur  at  the  same  moment  at  c',  and  a  rare- 
faction at  a',  consequently  there  would  be  like  conditions 
at  a  and  c',  and  opposite  conditions  at  c.and  a* ';  but  now 
the  wave  is  reflected  at  b,  cf  therefore  coincides  with  c, 
and  a'  with  a ;  condensation  and  rarefaction  will  conse-       " 
quently  cease  at  c  as  well  as  at  a ;  there  being  nothing 
at  these  points  but  a  simple  motion  backwards  and  for- 
wards of  the  layers  of  air,  without  any  marked  change  of 
density. 

Let  us  now  see  what  goes  on  at  c?.  I  va.  - 

If  the  maximum  of  density  be  advanced  from  a  to  d,  it 
would  also  have  gone  on  from  cf  to  df,  if  there  were  no 
reflection  at  6;  at  d  and  d1  there  are  consequently  always 
equal  conditions  of  oscillation ;  but  by  the  reflection  at  6, 
d'  is  thrown  upon  d ;  hence  the  maximum  of  the  density 
of  the  incident  and  reflected  waves,  and  \  an  undulation  N 
later,  the  maximum  of  the  rarefaction  of  both,  coincide; 
and  consequently  there  will  be  here  alternately  an  in- 
creased condensation  and  rarefaction. 

If,  now,  we  investigate  the  condition  of  oscillation  of  a 
layer  of  air  at  d,  we  shall  find  that  it  has  no  motion,  for 
if  the  waves  advanced  beyond  6,  there  would  be  equal 
conditions  of  oscillation  at  d  and  d',  which  wrould  always 
move  towards  the  same  side  with  uniform  velocity ;  but  if 
the  wave  system  be  reflected,  the  reflected  wave  of  the 
layer  of  air  d  will  impart  an  opposite  motion  to  that  which 
it  would  have  imparted  without  any  reflection  of  the  layer 
of  air  d'  •  d  is,  therefore,  always  affected  by  both  wave- 
systems  with  equal,  but  oppositely  directed  velocities; 
and  consequently  this  layer  of  air  must  remain  at  rest. 

The  Figs,  from  206  to  208  show  the  air-waves  formed 
in  a  tube  fths   of  the  length  of  the  incident   sound-      »- 
wave. 

In  Fig.  206  we  see  a  maximum  of  condensation  at  d,  and  a 
maximum  of  rarefaction  at  the  bottom  of  the  tube  at  6;  all  the 


232        LAWS    OF    THE    VIBRATIONS    OF   MUSICAL    TONES. 

Fig.  206. 


Fig.  20' 


Fig.  208. 


layers  of  air  lying  to  the  left  of  d,  simultaneously  begin  their 
motion  in  the  direction  indicated  by  the  arrow;  whilst  the  layers 
lying  to  the  right  of  c?,  begin  to  move  towards  the  right. 

After  J  of  an  undulation,  the  separate  layers  have  reached  such 
a  position  that  the  air  is  of  uniform  density  throughout  the  whole 
tube,  as  intended  to  be  represented  in  Fig.  207 ;  after  another  J 
of  an  undulation  moving  in  the  direction  indicated,  the  condition 
represented  in  Fig.  208  will  occur;  now  there  is  the  greatest 
condensation  at  b,  and  the  greatest  rarefaction  at  d. 

From  this  moment  the  separate  layers  of  air  again  begin  to 
move  towards  d,  and  then  the  condition  represented  in  Fig.  206 
recurs  after  J  of  an  undulation. 

The  layers  of  air  lying  to  the  right  and  left  of  e?,  either  move 
simultaneously  away  from,  or  simultaneously  towards  d,  which  has 
no  motion;  the  layer  of  air  d  forms,  therefore,  a  node  of  oscil- 
lation. 

The  point  c  and  a,  where  there  is  neither  rarefaction  nor  con- 
densation, but  where  the  layers  of  air  oscillate  with  the  greatest 
amplitude,  are  termed  bellies. 

In  order  to  put  the  air  within  a  closed  tube,  into  such  standing 
vibrations,  it  is  only  necessary  to  bring  an  oscillating  body  before 
the  open  extremity  of  the  tube,  which  may  give  such  a  tone,  that 
the  length  of  the  tube  is  equal  to  J,  f,  |,  &c.,  of  the  wave  length 
of  the  tone. 

We  may  use  for  this  purpose  an  ordinary  tuning-fork,  holding 
it  over  a  glass  tube  of  about  two  inches  in  length,  closed  below; 
or  we  may  take  a  glass  or  metal-plate  in  the  same  manner  as 


LAWS    OF    THE    VIBRATIONS    OF    MUSICAL    TONES.        233 

when  used  to  produce  Chladntfs  figures  by  the  help  of  the  bow  of 
a  violin,  holding  a  tube,  closed  below,  under  it.  If  the  tube  be 
of  the  right  length,  the  enclosed  air,  being  thrown  into  a  state  of 
standing  vibrations,  will  become  resonant,  considerably  increasing 
thereby  the  intensity  of  the  tone,  as  may  be  clearly  perceived  by 
passing  the  sounding  body  backwards  and  forwards  before  the 
opening  of  the  tube;  the  tone  becoming  alternately  stronger  and 
weaker  as  the  body  is  brought  to  the  opening  or  beyond  it.  If 
the  tube  should  be  too  long  for  the  sounding  body  that  is  used,  it 
may  easily  be  brought  in  accordance  with  it  by  pouring  water 
into  it;  that  is  to  say,  it  may  be  thus  shortened  until  it  have  the 
length  proper  for  the  sounding  body. 

In  order  to  throw  the  enclosed  air  into  regular  vibrations,  or  to 
make  it  resonant  with  the  sounding  body,  it  is  not  indispensably 
necessary  to  bring  a  sounding  body  before  the  opening  of  a  tube. 
Thus,  in  organ  pipes,  there  is  a  current  of  air  flowing  past  the 
open  end  of  the  tube,  breaking  against  the  edges,  and  creating,  by 
its  impulses,  waves  that  are  reflected  on  the  bottom,  and  interfere 
with  the  newly  incident  waves.  Although  these  impulses  are  at 
first  not  quite  regular,  they  are  soon  regulated  by  the  accession  of 
reflected  waves,  provided  the  tube  sound  well,  so  that  regularly 
standing  waves  are  formed,  by  means  of  which  the  air  in  the  tube 
becomes  resonant. 

The  notes  yielded  in  this  manner  by  a  tube,  are  of  the  same  kind 
as  those  which  must  be  given  forth  by  another  sounding  body 
brought  to  the  opening  of  the  tube  for  the  purpose  of  inducing 
spontaneous  sound  in  the  enclosed  air. 

The  simplest  way  of  making  air  sound  in  a  small  tube  is  by 
holding  it  in  a  vertical  position  before  the  mouth,  turning  the 
closed  end  downwards,  whilst  the  open  extremity  is  held  to  the 
lower  lip,  arid  we  blow  obliquely  towards  the  edge  of  the  tube. 

Notes  are  naturally  higher  in  proportion  to  the  shortness  of  the 
pipes.  Organ  pipes  have  generally  the  arrangement  represented 
in  the  following  figures.  We  divide  them  into  the  pedal,  yielding 
the  wind,  the  mouth  and  the  tube  containing  the  column  of  air, 
the  vibrations  of  which  produce  the  note.  The  pedal  is  hollow, 
(Figs.  209  to  213,)  and  through  this  cavity  the  wind  passes  by 
means  of  a  fine  slit  into  the  tube.  The  mouth-piece  b  b'  is  more 
or  less  open,  that  is  to  say,  its  upper  part  is  more  or  less  removed 

20* 


234 


OPEN   PIPES. 


from  the  lower,  and  not  unfrequently  the  former  is  movable,  so 
as  to  open  or  close  the  mouth-piece  at  will. 


Fig.  209.     Fig.  210. 


Fig.  211. 


Fig.  212. 


Fig.  213. 


I 


The  organ  pipes  are  filled  with  wind  by  means  of  bellows. 
If  air  be  blown  into  the  pedal  of  the  tube,  there  will  be  a  thin 
layer  formed  at  its  passage  from  the  air-hole,  breaking  against  the 
upper  lip,  and  thus  imparting  those  impulses  to  the  air  in  the  tube, 
which  occasion  the  notes. 

The  same  tube  closed  at  one  extremity,  may  yield  many  notes. 
The  deepest  having  a  wave-length  four  times  as  great  as  the  length 
of  the  tube ;  the  higher  notes  of  the  pipe  correspond  to  a  wave- 
length three  times,  five  times,  &c.  as  short  as  the  wave-lengths 
occasioned  by  standing  vibrations,  having  threet  imes,  five  times, 
&c.  as  short  a  duration  of  oscillation  as  the  deepest  note  of  the 
pipe. 

The  pipe  yields  the  deepest  note  with  a  faint  wind,  and  the 
highest  notes  with  a  strong  wind. 

Open  Pipes. — A  stronger  condensation  of  air  may  occur  at  the 
end  than  in  the  middle  of  the  pipe,  as  the  air  cannot  escape 
laterally  from  the  former.  If,  now,  the  condensed  portion  of  a  wave 
arrive  at  the  open  extremity  of  the  tube,  the  layers  of  air  may 
easily  escape  in  all  directions  on  their  passage  from  the  tube,  and 
a  rarefaction  thence  arise  ;  which,  being  reflected,  as  it  were,  from 
the  open  end  of  the  tube,  traverses  it  in  an  opposite  direction,  and 
so  standing  waves  are  here  formed. 


OPEN    PIPES. 


235 


The  returning  wave  is  naturally  not  so  intense  as  the  original 
one. 

As  a  condensation  always  coincides  with  a  rarefaction  at  the 
open  extremity  of  the  tube,  a  belly  must  necessarily  arise  here, 
while  nodes  of  oscillation  can  only  be  formed  in  the  interior  of  the 
tube. 

If  a  wave-length  I  belong  to  the  note  of  the  body  by  which  the 
air  in  the  tube  is  to  be  brought  to  sound,  the  length  of  the  shortest 

open  tube  corresponding  to  this  note  will  be  —  ;   that  is  to  say, 

the  tube  is  half  as  long  as  the  wave-length  of  its  note.  If,  there- 
fore, the  deepest  notes  of  one  open  and  one  covered  pipe  are  to  be 
equal,  the  open  pipe  must  be  twice  as  long  as  the  other. 

A  node  of  oscillation  occurs  in  the  middle  of  the  length  of  an 
open  tube  in  forming  the  deepest  note,  and  a  belly  at  each  ex- 
tremity, as  represented  in  Figs.  214  and  215. 

Fig.  214. 


Fig.  215. 


Fig.  214  represents  the  moment  when  the  greatest  condensation 
takes  place  in  the  middle  of  the  tube;  while  the  layer  of  air  re- 
mains at  rest  in  the  tube,  the  air  begins  to  move  away  on  both 
sides  from  the  middle,  as  indicated  by  the  arrow ;  rarefaction  is 
at  its  maximum  half  an  undulation  afterwards  in  the  middle  of  the 
tube,  and  now  the  layers  of  air  begin  to  move  towards  the  middle 
from  both  sides.  In  the  next  highest  note,  a  belly  occurs  in  the 
middle  of  the  tube,  and  nodes  at  the  points  a  and  b,  which  are  J 
of  the  length  of  the  tube  from  the  extremities.  If  condensation 
be  at  its  maximum  at  a,  as  represented  in  Fig.  216,  then  the 


Fig.  216. 


<   <sa^ 


236  MUSICAL    NOTES. 

rarefaction  will  be  at  its  maximum  at  b,  and  conversely  as  seen  in 
Fig.  217. 

Fig.  217. 

6 


In  the  above  case,  the  wave-length  of  the  note  is  equal  to  the 
length  of  the  tube,  while  the  duration  of  oscillation  of  this  note  is 
half  as  great  as  that  of  the  key-note  of  the  tube. 

The  third  tone  that  the  tube  can  give,  has  a  wave-length  1  \  times 
that  of  the  length  of  the  tube  ;  in  this  tone,  there  are  three  nodes 
of  oscillation,  one  of  which  lies  in  the  middle,  and  each  of  the 
remaining  two  at  i  of  the  length  of  the  tube,  or  |  of  the  wave- 
length of  the  engendering  sound-wave. 

If  we  designate  the  length  of  an  open  tube  by  /,  the  wave- 
lengths of  the  tones,  it  is  capable  of  yielding : 

2  /,  § ;,  §  /,  &.C., 

whilst 

4  /,  U  U  &C- 

are  the  wave-lengths  of  the  tones  that  can  be  produced  from  a 
covered  pipe  of  the  length  /. 

If,  now,  at  different  parts  of  an  organ-pipe,  we 
make  holes  that  can  be  closed  or  opened  at  will,  by 
a  slide,  as  represented  in  Fig.  218,  we  can  prove 
that  the  tone  will  not  be  changed  if  the  opening  be 
made  at  a  belly,  although  it  would  be  altered  were 
the  aperture  at  any  other  part. 

Musical  Notes. — As  we  have  now  learnt  to  know 
the  means  by  which  pure  notes  may  be  produced, 
as,  for  instance,  through  organ-pipes,  and  since  we 
have  seen  how  the  height  and  depth  of  these  notes 
depend  upon  the  length  of  the  pipes,  and  conse- 
quently that  we  may  accord  such  pipes  at  will,  by 
lengthening  or  shortening  the  tubes,  we  will  proceed 
to  consider  the  series  of  notes  made  use  of  in  music. 
Let  us  begin  with  the  fundamental  note  yielded 
by  a  covered  pipe,  4  feet  in  length ;  this  tone  is  designated  in 
music  as  the  note  C. 

If  we  examine  the  notes,  which,  combined  with  C,  will  make  an 


MUSICAL   NOTES.  237 

agreeable  impression  upon  the  ear,  we  shall  find  them  to  be  those 
whose  rapidity  of  oscillation  stands  in  a  certain  relation  to  that  of 
C;  their  wave-lengths  are  J,  J,  f-,  y,  £  of  the  wave-length  of  C; 
and  they  are  consequently  those  that  would  be  produced  by  pipes 
whose  lengths  are  J-,  f ,  f ,  £  of  the  length  of  the  pipe  C. 

As  the  time  of  oscillation  stands  in  an  inverse  proportion  to  the 
wave-length,  the  first  of  the  above-named  notes  will  make  two 
vibrations  while  C  makes  only  1 ;  this  note  is  the  octave  of  C,  and 
is  designated  as  c. 

The  note,  whose  wave-length  is  f  of  that  of  the  note  C,  makes 
3  oscillations  while  C  makes  2 ;  this  is  the  fifth  of  C,  and  is  de- 
signated as  G. 

The  note,  wrhose  wave-length  is  f  of  that  of  C,  makes  4  vibra- 
tions while  C  makes  3;  it  is  called  the  fourth  of  C,  and  is 
marked  F. 

The  note,  whose  wave-length  is  A  of  that  of  the  note  C,  makes 
5  vibrations  while  C  makes  4 ;  it  is  the  major  third  of  C,  and  is 
marked  E. 

The  last  note  to  be  mentioned,  and  whose  wave-length  is  f  times 
as  great  as  that  of  C,  makes  6  vibrations  while  C  only  makes  5 ; 
it  is  the  minor  third  of  C,  and  is  marked  E  flat. 

As  C  has  its  octave,  fifth,  fourth,  major  and  minor  third,  so 
there  are,  likewise,  an  octave,  a  fifth,  a  fourth,  and  a  major  and 
minor  third  for  c. 

The  fundamental,  or  key-note  C,with  its  major  third  E,  and  its 
fifth  G,  form  the  common  chord  of  C  major. 

According  to  the  above  relations,  the  notes  below  make  vibra- 
tions simultaneously,  as  follows: 

C  E  F  G  c 

24  30  32  36  48 

In  order  to  perfect  the  whole  series  of  notes,  E,  F  and  G  must 
have  their  accord,  consequently  their  third  and  fifth,  as  well  as  C. 

The  fifth  of  G  is  a  note  vibrating  3  times,  while  G  only  per- 
forms 2  vibrations;  there  are,  therefore,  to  36  vibrations  of  G,  54 
vibrations  of  its  fifth,  which  we  will  designate  as  d\  the  next  octave 
below  d  is  marked  D,  and  makes  27  vibrations  to  36  of  G,  and 
24  of  C. 

The  major  third  of  G,  designated  as  H9  must  make  five  vibra- 
tions, while  G  only  completes  4;  there  are,  therefore,  45  oscilla- 
tions ofHto  36  of  G. 


238  MUSICAL    NOTES. 

As  24  is  to  36,  (that  is,  C  to  G,)  as  32  is  to  48,  (or  F  to  c,)  c 
is  the  fifth  of  F. 

The  major  third  of  F  must  make  5  vibrations,  while  the  latter 
makes  only  4;  to  32  vibrations  of  F  there  will,  consequently,  be 
40  of  its  major  third,  which  we  designate  as  Ji. 

Thus  we  have  a  series  of  notes  bearing  the  name  of  the  C  gamut. 
The  simultaneous  vibrations  are  as  follows : 

CDEFGrfHcde&c. 
Vibrations:  24     27     30     32     36     40     45     48   54   60 

The  differences  between  each  two  succeeding  notes  of  this  series 
are  not  equal.     In  the  following  series,  the  somewhat  deeper  break 
between  two  numbers  indicates  how  much  the  rapidity  of  oscilla- 
tion of  each  note  exceeds  that  of  the  succeeding  one. 
C     D      E       F        G       A      H     c; 
-I      *     A       i       *       *    .iV 

D  accordingly  makes  1J  times  as  many  vibrations  in  the  same 
period  of  time  as  (7,  E  l£  times  as  many  as  D,  F  1TV  times  as 
many  as  E,  &c. 

The  interval  between  C  and  D,  between  D  and  E,  F  and  G,  G 
and  */?,  and  JL  and  H,  is  called  a  perfect  tone ;  we  distinguish  them, 
however,  as  full  perfect  tones  if  the  interval  be  j,  and  small  perfect 
tones  when  it  is  only  ^. 

The  intervals  between  E  and  F,  and  Jfand  c,  are  nearly  half  as 
large  as  the  rest ;  they  are,  therefore,  called  semi-tones. 

If  we  proceed  from  any  of  the  other  notes,  advancing  in  the 
same  order  of  intervals,  we  shall,  in  the  same  manner,  obtain  the 
various  gamuts  ;  in  order,  however,  to  proceed  according  to  this 
arrangement  of  intervals  for  each  note,  we  must  insert  half-notes 
between  Cand  D,  F  and  G,  and  G  and  H,  marking  them  thus  :  c 
sharp,  e  flat,  f  sharp,  g  sharp,  and  b. 

Through  the  gamuts  we  pass  from  the  key-note  to  the  major 
third ;  and  then,  passing  over  the  minor  third,  to  the  fifth ;  in  the 
soft-toned  gamuts,  on  the  contrary,  the  chord  is  formed  by  the 
key-note,  the  minor  third,  and  the  fifths. 

A  fuller  consideration  of  the  kinds  of  tone  and  the  gamut  belongs 
to  the  theory  of  music,  and  would  lead  us  beyond  our  limits. 

If  the  fundamental,  or  key-note,  make  1  vibration  in  a  given 
time,  the  major  third  must  make  f-  in  the  same  time ;  the  major 
third  of  this  note  will  make  £.f,  or  ft,  and  the  third  of  this  note 
I .  | .  f ,  or  VY  vibrations.  The  latter  note  does  not  exactly  accord 


MUSICAL    NOTES.  239 

with  the  octave  of  the  fundamental  note,  which  corresponds  to  W  ; 
if,  therefore,  we  proceed  through  full  thirds,  we  do  not  reach  a 
pure  octave  ;  and,  if  we  retain  the  purity  of  octaves,  we  must  ab- 
stract from  the  perfect  purity  of  thirds.  The  same  is  the  case  with 
respect  to  pure  fifths.  We  are,  therefore,  obliged  to  set  the  notes 
somewhat  higher  or  lower  than  required  for  pure  thirds  or  fifths, 
in  order  to  retain  the  purity  of  the  octave  ;  the  note  must  be  suf- 
fered, in  the  ordinary  language  of  musicians,  to  float  somewhat 
over  or  under.  This  mode  of  balancing  is  called  the  temperature. 
It  would  carry  us  too  far,  however,  to  treat  of  the  separate  kinds 
of  temperature. 

If  the  ear  were  more  sensitive  than  it  is,  it  would  be  so  unplea- 
santly affected  by  the  impurity  of  the  thirds  and  fifths,  as  almost  to 
preclude  any  enjoyment  from  music. 

As  we  have  now  become  better  acquainted  with  the  various  de- 
signations applied  to  notes,  we  may  use  them  in  speaking  of  the 
different  tones  yielded  by  the  same  pipe.  In  an  open  tube  or 
pipe,  for  instance,  the  second  note  is  the  octave  of  the  key-note, 
while,  in  a  covered  pipe,  it  is  the  fifth  of  the  next  higher  octave. 

The  deepest  tone  applied  in  music  is  that  yielded  by  a  covered 
pipe  16  feet  in  length.  But,  now,  we  know  that  when  a  covered 
pipe  gives  forth  its  deepest  notes,  its  wave-length  must  be  exactly 
J  of  the  wave-length  of  the  note ;  accordingly,  the  wave-length 
for  this  note  must,  in  an  ordinary  state  of  the  atmosphere,  be 
64  feet. 

Sound  travels  about  1,089  English  feet  in  a  second  (1125. 
Hershel);  if  we  divide  this  number  by  64,  we  find  how  many 
wave-lengths  this  deepest  note  advances  in  a  second ;  or,  what 
is  the  same  thing,  how  many  oscillations  are  necessary  in  a 
second  to  produce  this  deepest  musical  note;  we  find  the  number 
to  be  17.1. 

In  like  manner,  we  find  how  many  oscillations  the  air  makes 
in  a  second  in  a  covered  pipe  while  giving  its  deepest  note,  by 
dividing  four  times  the  length  of  the  pipe  (expressed  in  Paris 
feet),  by  1,050. 

Music  altogether  comprises  9  octaves.  The  deepest  note  already 
spoken  of,  yielded  by  a  covered  pipe  16  feet  in  length,  is  desig- 
nated as  C. 

As  this  note  makes  16,5  vibrations  in  a  second,  the  following 


240  TONES    OF    STRETCHED    STRINGS. 

table  gives  the  number  of  vibrations  for  each  of  the  successive 
octaves  of  this  tone : 


With  our  notes,  the  tones  are  thus  expressed : 


Tones  of  Stretched  Strings. — The  most  important  laws  of  the 
vibrations  of  stretched  strings  are  as  follows : 

1 .  The  number  of  vibrations  of  a  string  is  inversely  as  its  length  ; 
that  is,  if  a  string  of  any  instrument,  as  a  violin  or  a  guitar,  be 
stretched,  and  make  a  certain  number  of  vibrations  in  a  given 
time,  it  would  make  in  the  same  time  2,  3,  or  4  times  as  many 
vibrations,  if  with  the  same  tension  we  let  only  J,  ^,  or  \  of  .the 
whole  length  vibrate ;  it  would  vibrate  f ,  |,  or  f  times  as  fast  if 
we  only  suffered  f ,  f ,  or  f  of  the  whole  line  to  vibrate. 

2.  The,  number  of  the  vibrations  of  a  string  is  proportional  to 
the  square  root  of  the  stretching  weight;  that  is,  if  the  weight 
stretching  the  string  were  made  4,  9,  or  16  times  as  great  whilst 
the  length  remained  unaltered,  the  velocity  of  the  vibrations  would 
be  2,  3,  or  4  times  as  great. 

3.  The  number  of  vibrations  of  different  strings  of  the  same  sub- 
stance is  inversely  as  their  thickness.     If,  for  instance,  we  take 
two  steel  wires  of  equal  length,  whose  diameters  are  as  1  to  2, 
the  thinner  will  with  equal  tension  make  twice  as  many  vibrations 


TONES   OF   STRETCHED   STRINGS.  241 

as  the  thicker.     This  law  does  not  always  hold  good  for  catgut 
strings,  as  they  are  not  absolutely  made  of  the  same  substance. 

An  instrument  called  a  monochord  is  used  to  illustrate  the  most 
important  laws  of  stretched  strings  and  their  notes,  which  gives 
out  pure  notes,  and  admits  of  the  length  of  the  strings  being 
measured  with  great  exactness.     Fig.  219  represents  a  mono- 
Fig.  219. 


chord.  We  may  stretch  a  catgut  or  a  metal  string  to  prove  that 
both  follow  the  same  laws.  The  string  attached  at  c,  goes  over 
a  kind  of  bridge  at  f  and  A,  then  over  a  pulley  TTI,  being  finally 
loaded  with  the  weight  p.  The  movable  bridge  h  may  be  pushed 
along  without  touching  the  string,  and  secured  by  a  binding  screw 
to  any  part  we  choose.  We  shall  presently  see  how  the  hollow 
box  s  s'  serves  to  strengthen  the  note.  If,  now,  we  suppose  the 
string  to  be  sufficiently  stretched,  when  vibrating  freely,  to  give  a 
full  and  sure  note,  which  we  will  assume  to  be  the  starting  point 
of  c,  we  may,  by  moving  the  bridge,  make  the  string  yield  suc- 
cessively the  notes  d,  e,  f,  g,  a,  h,  and  c.  If  we  designate  the 
length  of  the  string,  giving  the  fundamental  note  c,  as  1,  we  shall 
obtain  the  following  lengths  of  string  for  the  other  notes : 
cdefgahc 

.1  f  *  *  I  I  TV  * 

We  must,  therefore,  make  the  string  half  the  length  in  order  to 
make  it  yield  the  octave,  other  conditions  remaining  the  same. 
But  as  the  octave  makes  twice  as  many  vibrations  as  the  funda- 
mental note,  a  string  half  the  length  will  make  double  the  number 
of  vibrations. 

To  obtain  the  fifth,  we  must  shorten  the  string  to  f  of  its  length ; 
but  the  fifth  makes  f  times  as  many  vibrations  as  the  fundamental 
note  in  an  equal  time. 

The  number  of  vibrations  of  strings  is,  therefore,  inversely  as 
their  length. 
21 


242       LAWS    OF    THE    VIBRATIONS    OF    BLADES    AND    RODS. 


To  obtain  an  octave  with  an  equal  length  of  string,  we  must 
Fig.  220.  attach  4  times  as  heavy  a  weight,  and  £ 

as  heavy  a  one  for  the  fifth. 

Laws  of  the  Vibrations  of  Blades  and 
Rods. — If  a  blade  or  rod  be  fastened  at 
one  end  (see  Fig.  220),  and  be  touched 
by  the  bow  of  a  violin,  or  simply  brought 
out  of  equilibrium  by  the  hand,  it  will 
make  a  series  of  vibrations  between  I 
and  lf,  which,  if  sufficiently  rapid,  will 
produce  a  note.  If  different  lengths  be 
given  to  the  same  blade,  the  number  of 
the  vibrations  made  in  a  given  time  will 
be  inversely  as  the  square  roots  of  the 
vibrating  lengths. 

Of  Reed-pipes. — A  tongue  is  generally 
a  vibrating  plate  set  in  motion  by  a  current  of  air. 

Let  p  (Fig.  221)  be  a  plate  of  metal  0.078  to  0.118  inch  in 
Fig.  221.  thickness,  having  a  rectangular  opening  a  b  c  d,  1.181 
inch  in  length,  and  from  0.275  to  0.314  inch  in  breadth, 
over  which  a  very  thin  elastic  brass  plate  is  fastened, 
as  represented  in  the  diagram.  This  plate  can  vibrate 
on  touching  the  edges  a  b,  b  c,  and  c  d.  In  this  man- 
ner we  have  a  very  simple  tongue-work,  which  can  be 
set  in  motion  by  putting  the  plate  p  lengthwise  to  the 
lips,  and  blowing  so  as  to  direct  the  air  against  the  free  end  of  the 
plate  /.  The  latter  is  made  to  vibrate  by  the  current  of  air;  the 
aperture  is  alternately  opened  and  closed  while  the  current  first 
pours  in,  and  then  is  checked  in  its  course  ;  in  this  manner  sound- 
waves arise,  whose  length  depends  upon  the  number  of  vibrations 
which  the  dimensions  and  elasticity  of  the  plate  I  admit  of  its 
making  in  a  given  time.  With  the  exception  of  greater  intensity, 
the  note  is  the  same  as  if  the  plate  were  made  to  vibrate  by  me- 
chanical means.  If  we  fasten  several  such  bars  to  one  plate, 
choosing  such  as  will  yield  the  succeeding  notes  of  a  gamut,  we 
may  make  an  instrument  on  which  we  may  play  various  tunes. 

The  tongue- work  of  an  organ  depends  upon  similar  principles, 
although  in  this  case  the  tongue  is  differently  attached.  Here  we 
distinguish  two  contiguous  tubes,  t  and  tf  (Fig.  224),  a  stop  b 
dividing  them,  and  the  actual  tongue-piece  passing  through  the 


REED-PIPES. 


243 


222. 


Fig.  223. 


stop.     The  tongue-work  itself  is  represented  on  a  larger  scale  in 
Fig.  223,  and  consists  essentially  of 
three  parts,  the  channel  r,  the  tongue 
/,  and  the  tuning-wire  z. 

The  channel  is  a  prismatic,  or  half 
cylindrical  tube,  closed  below,  and 
open  at  the  top,  having  an  aperture 
at  the  side  by  which  both  tubes  are 
joined  together. 

The  tongue  is  the  vibrating  plate ; 
in  its  natural  position,  the  lateral 
opening  of  the  channel  is  either  en- 
tirely or  almost  closed  by  it ;  that  is 
to  say,  it  touches  upon  the  edges  of 
the  opening  with  its  three  free  edges 
during  its  oscillations ;  the  fourth  side 
being  secured  to  the  tube  either  by  a 
screw  or  by  soldering. 

The  tuning-wire  is  a  strong  metal  wire,  doubly  curved  below, 
and  pressed  against  the  tongue  along  its  whole  breadth.  It  may 
be  pushed  up  and  down  in  the  stop  with  some  friction,  and  thus 
the  vibrating  portion  of  the  tongue  may  be  lengthened 
or  shortened,  for  the  part  over  the  tuning- wire  cannot 
vibrate. 

The  wind  of  the  bellows  enters  through  the  pedal  of 
the  tube  tf9  and  pressing  against  the  tongue  to  procure 
an  outlet,  forces  itself  through  the  channel,  and  escapes 
from  the  tube  t.  The  tongue,  thus  brought  out  of  its 
equilibrium,  returns  immediately  by  means  of  its  elas- 
ticity, making  vibrations  in  this  manner,  which  last  as 
long  as  the  current  of  air  continues.  Fig.  222  repre- 
sents a  reed-pipe  in  which  the  part  of  the  tube  opposite 
to  the  tongue  is  of  glass,  the  better  to  show  its  working. 

In  organs  the  reed-pipes  are  often  constructed  some- 
what differently,  by  the  edges  of  the  tongue  striking 
upon  the  edges  of  the  channel,  as  exhibited  in  Fig.  224. 

If  a  reed-pipe  vibrate  of  itself  in  free  air — if,  conse- 
quently, no  pipe,  or  only  a  relatively  short  one,  be 
placed  over  it,  its  rapidity  of  vibration,  and  therefore  its  note, 


Fig.  224. 


244  TRANSMISSION    OF    VIBRATIONS    OF    SOUND. 

depend  upon  its  elasticity  and  dimensions ;  if,  however,  a  long 
tube  be  put  on,  it  will  essentially  modify  the  note ;  the  motion  of 
the  tongue  depends,  therefore,  more  upon  the  motion  of  the  air- 
waves passing  backwards  and  forwards  in  the  long  pipe  than 
upon  its  own  elasticity;  it,  therefore,  vibrates  less  of  itself  than 
from  external  agents. 

Transmission  of  vibrations  of  sound  between  solid,  fluid,  and 
aeriform  bodies. — If  several  solid  bodies  be  united  together  in  a 
whole,  the  vibrations  issuing  from  one  part  of  this  system,  distri- 
bute themselves  with  the  greatest  ease,  as  advancing  waves  over 
the  whole  mass  ;  having  reached  the  confines,  the  waves  pass  only 
partially  into  the  contiguous  medium,  the  aeriform  or  fluid  body ; 
they  are  partially  reflected,  however,  and  regular  vibrations  are 
formed  in  the  separate  parts  of  the  solid  system  by  the  interference 
of  the  reflected  with  the  fresh  incident  waves.  Such  a  system 
forms  a  whole,  which,  if  a  point  be  made  to  vibrate,  will  be  like 
a  single  solid  body  divided  into  separate  vibrating  parts,  divided 
by  nodes  of  oscillation.  Each  separate  part  loses,  to  a  certain 
degree,  its  individuality,  while  its  connection  with  the  contiguous 
parts  hinders  it  from  vibrating  as  it  would  do  if  it  were  isolated. 

While  sound-waves  are  easily  distributed  over  a  system  of  solid 
bodies,  they  pass  less  easily  from  a  solid  to  a  liquid,  and  with  still 
less  facility  to  a  gasiform  body ;  thus  it  happens  that  many  strongly 
vibrating  solid  bodies  only  yield  a  very  weak  tone,  owing  to  their 
inability  properly  to  impart  their  vibrations  to  the  air.  This  is  the 
case  with  the  tuning-fork,  for  instance,  which  gives  forth  only  a 
faint  sound  on  being  struck  with  force,  and  held  free  in  the  air. 

In  order  to  heighten  the  tone  of  such  a  body,  the  transmission 
of  its  vibrations  through  the  atmosphere  must  be  increased  by 
resonance,  that  is,  by  endeavoring  to  transfer  the  regular  vibra- 
tions of  the  sounding  body  to  another.  One  means  with  which  we 
are  already  acquainted,  is  to  bring  the  low-toned  but  strongl 
vibrating  body  before  a  tube  of  proper  length,  and  to  cause  th< 
enclosed  air  to  sound. 

A  second  method  of  strengthening  the  tone,  is  by  bringing  the 
sounding  body  in  contact  with  another  of  proportionately  l 
surface,  and  capable  of  being  readily  made  to  vibrate.  There  ai 
then  regular  sound-waves  formed  upon  it,  as  we  have  already  men- 
tioned, which  are  more  readily  transmitted  to  the  air,  owing  to  the 
large  area  of  the  sounding  (resonant)  body.  If,  for  instance,  w< 


TRANSMISSION    OF    VIBRATIONS    OF    SOUND.  245 

put  the  strongly  struck  tuning-fork,  which  yielded  in  the  open  air 
but  a  faint  sound,  upon  a  box  of  thin  elastic  wood,  the  note  will  be 
given  with  much  more  intensity.  On  this  principle  depends  the 
sounding-board  used  in  different  musical  instruments.  In  flutes, 
organ-pipes,  &c.,  no  such  application  is  necessary,  as  the  regular 
vibrations  of  a  mass  of  air  yield  the  note,  and  easily  distribute 
themselves  through  the  surrounding  atmosphere. 

As  vibrations  of  solid  bodies  create  sound-waves  in  the  air,  so, 
likewise,  sound-waves  may,  when  diffusing  themselves  through  the 
atmosphere,  cause  a  solid  body  to  vibrate  by  coming  in  contact 
with  it.  Thus,  for  instance,  we  see  the  string  of  an  instrument 
vibrate  if  it  come  in  contact  with  the  sound-waves  of  the  note  it 
yields,  or  with  those  of  one  of  its  harmonic  notes ;  and  in  this 
manner  the  panes  of  glass  in  a  window  shake  with  violence  from 
the  influence  of  certain  notes  of  the  voice,  or  from  the  report  of  a 
cannon.  This  phenomenon,  which  is  strikingly  manifested  in 
susceptible  bodies,  also  occurs  in  larger  masses  and  in  less  elastic 
bodies ;  all  the  pillars  and  walls  of  a  large  church  shake  more  or 
less  strongly  during  the  ringing  of  the  bells. 


21 


246  THE    ORGANS    OF    SPEECH. 


CHAPTER    III. 

OF  THE  VOICE  AND  HEARING. 

The  Organs  of  Speech. — It  is  well  known  that  the  wind-pipe  is 
a  tube  ending  at  one  extremity  in  the  throat,  and  at  the  other  in 
the  lungs.  Its  especial  use  is  to  give  a  free  passage  to  air  both 
in  inspiration  and  expiration;  it  is  almost  cylindrical,  being  com- 
posed of  cartilaginous  rings,  which  are  united  together  by  flexible 
membranous  rings.  At  its  lower  extremity,  it  separates  into  two 
tubes,  the  bronchi,  one  of  which  goes  to  the  right,  the  other  to  the 
left.  Each  of  these  branches  is  further  ramified  in  all  directions 
in  the  tissue  of  the  lung.  At  its  upper  end  the  wind-pipe  termi- 
nates in  the  larynx,  which  is  essentially  the  organ  of  speech. 

The  larynx  consists  of  four  cartilages,  which  ossify  in  extreme 
old  age ;  they  are  the  cricoid,  the  thyroid,  and  the  two  arytenoid 
cartilages.  These  cartilages  are  connected  with  one  another,  and 
likewise  with  the  upper  rings  of  the  wind-pipe,  and  may  be  moved 
in  the  most  varied  ways  by  means  of  different  muscles.  The 
inner  wall  of  the  larynx  forms  a  prolongation  of  the  wind-pipe, 
contracting  until  it  becomes  nothing  more  than  a  mere  chink, 
directed  backward,  known  as  the  glottis. 

The  edges  of  the  glottis  are  principally  formed  by  the  chordce 
vocales,  which  merge  anteriorly  in  the  thyroid  cartilage,  while,  at 
the  opposite  extremity,  one  chorda  vocalis  is  incorporated  in  the 
other,  and  the  second  to  the  other  arytenoid  cartilage,  so  that 
according  as  the  cartilages  are  brought  nearer  to,  or  further  from 
each  other  by  the  corresponding  muscles,  the  chordae  vocales 
become  more  or  less  stretched,  while  the  glottis  diminishes  or 
enlarges.  The  chordae  vocales  themselves  consist  of  a  very  elastic 
tissue. 

Above  the  edges  of  the  glottis  there  are  two  sac-like  cavities, 
one  to  the  right,  the  other  to  the  left  side,  stretching  from  eight  to 
nine  lines  laterally,  and  having  a  depth  of  five  or  six  lines ;  these 
are  the  ventriculi  morgagni.  The  upper  edges  of  these  ventricles 


THE    ORGANS    OF    SPEECH. 


247 


rm,  as  it  were,  a  second  glottis,  lying  five  or  six  lines  above  the 
other.  The  upper  glottis  may  be  covered  by  the  epiglottis,  which 
is  an  almost  triangular  membrane,  or  rather  a  cartilage;  it  is 
attached  to  the  glottis  anteriorly,  and,  when  covering  it,  hinders 
all  food  and  drink  from  getting  into  the  wind-pipe,  since  they 
must  pass  over  it  to  enter  the  oesophagus. 

The  formation  of  the  larynx  will  be  more  clearly  illustrated  by 
the  accompanying  figures.  Fig.  225  presents  an  anterior  view  of 
it;  Fig.  226  gives  a  lateral  view;  Fig.  228  gives  a  posterior,  and 
Fig.  227  a  superior  view,  leaving  out  the  muscles  that  move  the 


Fig.  225. 


Fig.  226. 


Fig.  227. 


Fig.  228. 


248  THE    ORGAN    OF    HEARING. 

cartilages,  and  thus  stretch  the  chordae  vocales.  In  all  these 
figures  the  cricoid  cartilage  is  designated  by  a,  the  thyroid  carti- 
lage by  bj  the  arytenoid  cartilages  by  c,  and  the  epiglottis  by  d. 
The  latter  is  represented  turned  upwards  to  show  it  more  dis- 
tinctly. In  Fig.  227  we  see  the  glottis  formed  by  the  two  lower 
chordae  vocales  stretched  between  the  thyroid  and  the  arytenoid 
cartilages.  In  this  figure  we  also  see  the  upper  chordae  vocales, 
together  with  the  ventriculi  morgagni,  lying  between  them  and  the 
lower  chordae  vocales. 

The  formation  of  notes  in  the  larynx  is  quite  similar  to  that  of 
reed-pipes.  A  tongue-work  depends  upon  this  principle,  that  a 
body  yielding  on  a  blow,  either  no  notes,  or  such  only  as  are  very 
faint  and  soundless,  may,  by  continual  impulses  of  the  air,  create  a 
note  corresponding  to  its  length  and  elasticity.  In  the  larynx  the 
vibrations  of  the  chordae  vocales,  by  which  the  glottis  is  closed  and 
opened  in  rapid  alternations,  occasion  the  notes,  as  we  may  easily 
see  by  the  following  contrivance  made  to  imitate  the  larynx. 

Cut  a  piece  measuring  about  1J  inches  from  a  thin  plate  of 
caoutchouc,  and  let  it  be  of  sufficient  breadth  to  be  folded  round 
a  glass-tube  about  six  or  seven  lines  in  diameter;  lay  this  so  round 
the  glass  cylinder  that  one-half  may  surround  the  latter,  and  the 
other  half  project  beyond  it;  if  we  bring  the  two  freshly  cut 
edges  of  the  caoutchouc  together,  they  will  adhere  firmly,  and 
we  thus  obtain  a  caoutchouc  cylinder  fastened  to,  and  projecting 
beyond  the  glass  cylinder,  to  which  it  must  be  secured  in  the 
manner  represented  in  Fig.  229.  If,  now,  we  fasten  the  caoutchouc 
Fig.  229.  cylinder,  at  its  upper  extremity,  to  two  sepa- 

rate points,  pulling  it  apart,  a  chink  will  be 
formed  (as  seen  in  the  figure)  with  caoutchouc 
edges,  and  if  we  blow  into  the  pipe  superiorly, 
we  obtain  a  tone  which  is  high  in  proportion 
to  the  force  exerted  by  the  lips.  We  may  thus 
clearly  see  the  vibrations  of  the  two  caout- 
chouc projections  forming  the  chink. 

The  height  and  depth  of  the  tones  of  the 
larynx  likewise  depend  upon  the  tension  of 
the  chordae  vocales. 
The  Organ  of  Hearing  consists  of  three  main  parts :  the  outer 
ear  formed  by  the  pinna,  and  the  external  meatus,  the  cavity  of 
the  tympanum  separated  from  the  above  meatus,  by  the  membrane 


THE    ORGAN   OF   HEARING.  249 

of  the  tympanum,  and  the  labyrinth.  The  labyrinth  consists  of 
osseous  cavities  filled  with  a  fluid,  and  through  which  the  auditory 
nerve  is  distributed  ;  in  order  to  enable  these  nerves  to  act,  the 
sound- vibrations  of  the  fluid,  which  is  wholly  surrounded  by  bones, 
must  be  transmitted  into  the  labyrinth ;  this  is  effected  by  two 
openings  of  the  labyrinth  leading  into  the  cavity  of  the  tympanum  ; 
they  are  termed  the  fenestra  ovalis  and  the  fenestra  rotunda ;  the 
latter  is  covered  with  a  tender  membrane,  while  the  former  has  a 
small  bone  inserted  into  it,  by  means  of  a  membranous  investment. 
This  bone,  which  is  termed  the  stapes,  we  shall  describe  more 
fully. 

Fig.  230  represents  the  labyrinth  on  an  enlarged  scale,  and 

Fig.  230. 


partly  opened.  It  consists  of  three  parts,  the  cochlea,  the  vesti- 
bule, and  the  semi-circular  canals.  The  auditory  nerve  is  dis- 
tributed partly  in  the  vestibule,  where  it  rests  on  the  ampullse,  the 
tubes  lining  the  semi-circular  canals,  and  filled  with  a  peculiar 
fluid;  and  more  especially  in  fine  ramifications  to  the  cochlea. 
The  convolutions  of  the  cochlea  are  separated  into  two  parts  by 
a  fine  osseous  partition-wall  running  parallel  to  one  of  these  con- 
volutions. This  wall  is  very  porous  and  cellular,  and  ramifica- 
tions of  the  auditory  nerve  terminate  in  these  cells,  as  may  be 
seen  in  the  exposed  part  of  the  cochlea  in  our  figure. 

The  sound- vibrations  are  conveyed,  by  means  of  the  little  bones 
in  the  cavity  of  the  tympanum,  to  the  labyrinth.  These  bones  are 
the  malleus,  which  with  its  handle  grows  into  the  side  of  the 
membrane  of  the  tympanum ;  the  incus  joining  the  malleus  and 


250  THE   ORGAN    OP    HEARING. 

connected  with  the  stapes  through  the  os  orbiculare  ;  the  stapes 
closing  the  fenestra  ovalis.  The  relative  position  of  all  these 
parts  may  be  seen  in  Fig.  231,  representing  the  labyrinth  on  a 
very  much  enlarged  scale ;  a  is  the  external  meatus  that  conveys 

Fig.  231. 


the  sound-waves  from  the  concha  to  the  membrane  of  the  tym- 
panum. This  latter  divides  the  cavity  of  the  tympanum  from  the 
external  meatus.  The  tympanic  cavity  is  connected  by  the  Eus- 
tachian  tube  b  with  the  cavity  of  the  mouth,  by  which  means  the 
air  in  the  former  cavity  can  always  be  in  equilibrium  with  the 
external  air ;  d  is  the  malleus,  attached  on  one  side  to  the  mem- 
brane of  the  tympanum,  while  on  the  other  side  it  is  inserted  into 
the  incus  e\  f  is  the  stapes,  which,  as  we  see,  closes  the  fenestra 
ovalis ;  o  is  the  fenestra  rotunda ;  n  is  the  auditory  nerve  distri- 
buted through  the  labyrinth. 

The  separate  parts  of  the  organ  of  hearing  do  not  lie  so  free  as 
might  appear  from  Fig.  231 ;  the  osseous  casing  which  encloses  the 
whole  being  omitted  for  the  sake  of  giving  distinctness  to  the 
figure.  The  external  meatus  itself  passes  through  the  temporal 
bone,  the  cavity  of  the  tympanum  is  surrounded  by  osseous  walls, 


THE   ORGAN   OF   HEARING. 


251 


Fig.  232. 


and  the  labyrinth  is  formed  in  a  part  of  the  temporal  bone,  called, 
on  account  of  its  hardness,  the  petrous  portion,  from  which  it  can 
only  be  separated  with  difficulty.  In  order  to  afford  a  correct  idea 
of  the  separate  parts  of  the  organ  of  hearing,  and  the  manner  in 
which  they  grow  in  the  osseous  mass,  we  have  given  at  Fig.  232 
an  actual  anatomical  section  of  the  parts,  represented  according  to 
their  natural  size ;  a  is 
the  section  of  the  coch- 
lea, b  one  of  the  semi- 
circular canals,  n  the 
nerve,  i  the  membrane 
of  the  tympanum  ;  the 
malleus,  incus,  and 
stapes,  are  also  clearly 
defined. 

The  pinna  serves  to 
receive  the  air-waves, 
and  conduct  them 
through  the  meatus  to 
the  membranes  of  the 
tympanum ;  the  latter 
is  thus  put  into  vibra- 
tions which  are  trans- 
mitted through  the  ossi- 
cles, and  through  the 
air  in  the  cavity  of  the 
tympanum  to  the  la- 
byrinth. The  mem- 
brane of  the  tympanum 
may  be  made  more  or 

less  tense,  and  drawn  inwards  by  means  of  the  muscle  £;  while, 
by  the  muscle  s,  the  stapes  may  be  moved,  and  the  intensity  of 
the  sound,  therefore,  considerably  modified. 

The  most  essential  part  of  the  organ  of  hearing  is  the  auditory 
nerve;  hence,  the  membrane  of  the  tympanum  may  be  injured,  and 
the  series  of  the  ossicles  broken  without  the  hearing  wholly  ceasing; 
in  many  of  the  lower  animals,  as  in  the  crab,  the  organ  of  hearing 
consists  merely  of  a  vesicle  filled  with  fluid,  in  which  the  vessel  of 
hearing  is  distributed. 


252  OF    LIGHT. 


SECTION  V. 


INTRODUCTION. 

OF  LIGHT. 

THE  most  casual  observation  teaches  us  that  a  luminous  point 
sends  its  light  in  all  directions ;  a  burning  taper,  for  instance, 
placed  in  the  centre  of  a  spherical  surface,  would  be  visible  from 
all  points  of  that  surface ;  the  same  is  the  case  with  regard  to  a 
phosphorescent  body,  an  electrical  spark,  &c.  What  is  evident 
to  our  common  experience  on  a  small  scale,  takes  place  alike  in 
the  vast  expanse  of  heaven.  The  sun  sheds  its  light  in  all  direc- 
tions of  space  ;  its  light  reaches  simultaneously  the  earth  and  the 
other  planets,  the  comets,  and  all  the  other  bodies  of  the  firma- 
ment, be  their  position  what  it  may  in  the  boundless  space  of 
heaven. 

All  luminous  bodies  consist  essentially  of  ponderable  matter; 
a  vacuum  may  transmit,  but  it  cannot  engender  light.  All  com- 
mon bodies  admit  of  being  divided  into  smaller  and  still  smaller 
particles,  and  the  ultimate  physically  perceptible  atoms  are 
termed  luminous  points.  As  everybody  is  an  assemblage  of  mole- 
cules or  atoms,  so  is  a  luminous  body  an  assemblage  of  luminous 
points. 

Bodies  which  are  not  self-luminous  are  divided  into  opaque,  as 
wood,  stones,  metals ;  transparent,  as  air,  water,  glass  ;  and  trans- 
lucent, as  thin  paper  and  ground  glass. 

Opaque  bodies  do  not  suffer  light  to  pass  through  their  mass ; 
but  opacity  always  depends  upon  the  thickness  of  the  body,  for  all 
bodies  will  admit  of  the  passage  of  some  degree  of  light  if  we 
make  them  sufficiently  thin.  For  instance,  we  may  perceive  a 
bluish-green  light  through  a  thin  gold  leaf  glued  on  a  glass  plate, 
if  we  hold  it  to  a  taper,  or  up  to  the  light. 


SHADOWS  AND  HALF  SHADOWS.  253 

Transparent  bodies  yield  a  passage  to  light,  and  allow  of  our 
seeing  with  distinctness  the  form  of  objects  beyond  them.  Gases, 
fluids,  and  most  crystalized  bodies  appear  to  be  perfectly  transr 
parent  when  taken  in  small  quantities  ;  for,  in  this  case,  they  seem 
to  be  wholly  colorless,  and  not  only  admit  of  our  seeing  the  form, 
but  also  the  color  of  objects  :  transparent  bodies  appear,  however, 
to  be  colored  if  they  are  thick — a  proof  that  they  must  absorb 
some  portion  of  light.  A  drop  of  water,  for  instance,  appears 
wholly  colorless,  whilst  the  same  fluid,  taken  in  a  mass,  has  a 
well-marked  green  hue. 

Translucent  bodies  admit  of  the  transmission  of  some  portion 
of  light,  without,  however,  allowing  the  form  or  color  of  objects 
being  recognized.  As  long  as  a  ray  of  light  remains  in  the  same 
medium,  it  advances  in  a  straight  line  ;  but,  as  soon  as  it  comes  in 
contact  with  another  body,  it  is  partly  thrown  back,  reflected  from 
its  surface ;  it  partly,  however,  enters  the  body,  if  it  be  transparent, 
in  an  altered  direction,  and  is  then  refracted.  We  shall  consider  the 
subject  of  reflection  and  refraction  more  fully  in  a  subsequent  page. 

The  velocity  with  which  light  travels  is  so  great,  that  it  tra- 
verses all  distances  upon  earth  in  an  imperceptibly  small  space  of 
time.  By  means  of  observations  on  the  eclipses  of  Jupiter's  satel- 
lites, astronomers  have  ascertained  that  light  is  transmitted  with 
such  velocity  as  to  traverse  the  space  between  the  sun  arid  the 
earth  in  eight  minutes  and  thirteen  seconds,  passing,  consequently, 
over  195,000  English  miles  in  one  second.  A  cannon  ball  going 
at  the  rate  of  1200  feet  in  a  second  would  require  fourteen  years 
to  go  from  the  sun  to  the  earth. 

Shadows  and  half  Shadows. — A  consequence  of  the  straight 
transmission  of  light  is,  that  a  dark  body  exposed  to  rays  of  light, 
throws  a  shadow ;  if  only  lighted  by  a  single  luminous  body,  it 
is  easy  to  define  the  shadow.  The  totality  of  all  the  lines 
issuing  from  the  luminous  Fig.  233. 

point,  and  striking  the  dark 
body,forms  a  conical  surface, 
and  the  part  of  it  lying  beyond  the  dark  body  forms  the  limits  of 
the  shadow. 

If  the  luminous  body  have  any  considerable  expansion,  there 

will  be  a  half  shadow  distinguishable  beyond  the  true  shadow. 

The  shadow,  which  in  this  case  is  the  central  shadow^  is  the 

.space  receiving  no  light ;  the  half  shadow,  on  the  contrary,  is  the 

22 


254 


SHADOWS  AND  HALF  SHADOWS. 


aggregate  of  all  the  spots  receiving  light  from  some  luminous 
points,  but  not  from  others.  Let  A  (Fig.  234)  be  a  large  lumi- 
nous sphere,  B  a  small  opaque  one.  The  figure  clearly  shows  the 

Fig.  234. 


Fig.  235. 


extent  of  the  true  shadow  and  the  half-shadow.  The  shadow 
would  assume  the  appearance  shown  at  Fig.  235,  if  received  upon 
a  screen  mf  n.  The  diameter  of  the  true  shadow 
diminishes  with  the  distance  of  the  luminous 
body,  while  the  diameter  of  the  half  shadow 
increases.  The  true  shadow  is,  therefore,  sur- 
rounded by  a  narrow  half  shadow,  close  to  the 
shading  bodies ;  close  to  the  back  of  the  shading 
body,  the  outline  is  somewhat  sharply  defined ; 
at  an  increased  distance,  the  width  of  the  half 
shadow  is  more  considerable,  and  the  transition  from  the  true 
shadow  to  the  full  light,  on  that  account,  more  gradual,  while  the 
shadow,  instead  of  being  sharply  defined,  seems  imperceptibly 
disappearing.  Beyond  the  point  s,  the  true  shadow  entirely 
ceases,  and  the  half  shadow,  increasing  continually  in  breadth, 
becomes,  on  that  account,  fainter  and  more  undefined. 

In  this  manner  we  may  understand  how  the  shadow  of  a  body 
exposed  to  the  sun's  light,  is  sharply  defined  close  behind  it,  while 
at  a  greater  distance  it  becomes  quite  undefined.  Thus,  for 
instance,  we  cannot  accurately  mark  the  point  where  the  shadow 
of  the  apex  of  a  steeple  is  lost  upon  the  ground.  A  hair  held  up 
in  the  sunlight  close  to  a  sheet  of  paper  will  cast  a  sharp  shadow, 
while,  if  held  two  inches  from  it,  a  shadow  is  scarcely  to  be  ob- 
served. If,  now,  the  light  issuing  from  a  luminous  point  be  thrown 
upon  a  screen,  through  which  a  small  aperture  has  been  made, 


SHADOWS   AND   HALF   SHADOWS. 


255 


the  light  passing  through  this  opening  will  form  a  well  defined 
ray ;  if  we  let  this  ray  fall  upon  a  second  screen,  we  shall  have  a 
luminous  spot  upon  a  dark  ground.  In  this  manner,  we  obtain 
on  the  wall  of  a  perfectly  dark  room  opposite  to  a  minute  aper- 
ture in  the  shutter,  an  image  of  an  external  luminous  point,  send- 
ing rays  of  light  through  the  aperture  into  the  chamber,  and  thus 
inverted  images  of  all  external  objects  may  be  thrown  upon  a 
wall  (Fig.  236).  If  we  allow  the  light  of  the  sun  to  pass  through 

Fig.  236. 


a  small  opening,  we  shall,  at  all  times,  have  a  round  image  of  the 
sun,  let  the  shape  of  the  opening  be  what  it  may.  This,  at  first 
sight,  apparently  strange  fact,  admits  of  a  simple  explanation.  If 
the  sun  were  a  single  luminous  point,  a  light  spot  would  be  formed 
upon  the  wall  opposite  to  the  opening,  and  having  precisely  the 
form  of  that  opening.  If  we  assume  that  the  opening  o  (Fig. 
237)  is  quadrangular,  the  light  passing  from  the  highest  point  of 

Fig.  237. 


the  sun's  disc  will  fall  upon  the  screen  in  the  direction  s  o  n, 
while  a  small  quadrangular  light  spot  will  appear  at  n.  The 
lowest  point  of  the  sun  occasions  a  quadrangular  image  at  n'f, 
while  the  middle  point  of  the  sun's  disc  forms  the  angular  figure  n'. 
The  image  /  comes  from  the  extremest  point  of  the  right  limb  of 
the  sun,  and  r  from  the  extreme  point  of  the  left.  All  the  other 
points  of  the  sun's  limb  give  quadrangular  figures,  falling  upon 
the  circumference  of  the  circle  /  n"  r  n,  whilst  the  remaining 


256 


THE    INTENSITY   OF    LIGHT    DIMINISHES 


points  of  the  sun  illuminate  the  interior  of  this  circle;  the  aggre- 
gate of  all  the  separate  quadrangular  bright  images  forms  conse- 
quently a  circular  illuminated  spot. 

The  intensity  of  Light  diminishes  inversely  as  the  square  of  the 
distance. — If  we  suppose  a  luminous  point  in  the  middle  of  a 
hollow  sphere,  its  surface  will  receive  all  the  light  issuing  from 
the  point.  If  the  same  luminous  point  were  in  the  middle  of  a 
hollow  ball  of  two  or  three  times  as  large  a  radius,  the  surfaces  of 
this  larger  ball  will  receive  all  the  light  issuing  from  the  point. 
But  geometry  teaches  us  that  the  surfaces  of  spheres  are  as  the 
squares  of  their  radii ;  if,  therefore,  the  radii  of  a  sphere  are  as 
1  :  2  :  3,  the  surfaces  will  be  as  1  :  4  :  9.  Thus,  if  the  same  lumi- 
nous point  be  in  a  sphere  of  2  or  3  times  as  great  a  radius,  the 
same  quantity  of  light  must  spread  itself  over  a  surface  4  or  9 
times  as  great ;  the  intensity  of  the  light  will  consequently  be  4 
or  9  times  less,  if  the  illuminated  surfaces  be  at  2  or  3  times  as 
great  a  distance  from  the  luminous  point:  that  is  to  say,  in 
general  terms :  the  intensity  of  light  diminishes  in  proportion  as 
the  squares  of  the  distances  increase. 

This  proposition  is  not  strictly  applicable  to  a  luminous  body  of 
considerable  surface,  whose  light  is  taken  up  from  a  small  distance. 

On  this  is  based  the  comparison  of  the  intensity  of  light  yielded 
by  different  sources.  In  Fig.  238  C  D  represents  a  white  wall. 

Fig.  238. 


Immediately  before  it  there  is  placed  an  opaque  rod  somewhat 
thicker  than  a  pencil ;  if,  now,  there  be  a  light  at  /  and  another  at 
jL,  two  shadows  of  the  rod  will  be  seen  upon  the  wall,  one  at  */?, 
the  other  at  B. 

The  part  of  the  wall  free  from  shadow  is  lighted  by  /  and  L, 
while  the  shadow  A  is  only  illuminated  by  the  light  /  and  B  by 


INVERSELY   AS   THE   SQUARE   OF   THE   DISTANCE.         257 

the  light  L.  If,  now,  both  sources  of  light  are  precisely  alike, 
both  shadows  will  appear  equally  dark,  provided  the  two  lights 
are  at  equal  distances.  But  if  L  yield  more  light  at  an  equal 
distance,  the  shadow  B  will  be  less  dark  than  ^?,  and  in  order  to 
make  both  shadows  alike,  it  would  be  necessary  to  remove  L 
further  from  the  screen. 

If  we  assume  that  L  were  really  so  far  removed  that  both 
shadows  were  again  made  equal,  the  intensity  of  light  yielded  by 
the  two  flames  would  be  as  the  squares  of  their  distances  from  the 
screen ;  if,  therefore,  L  were  two  or  three  times  further  from  the 
screen  than  I,  the  intensity  of  light  from  L  would  be  four  or  nine 
times  as  great  as  that  of  /. 


22* 


258  REFLECTION   OF    LIGHT. 


CHAPTER   I. 

REFLECTION   OF  LIGHT. 

Reflection  of  Light  from  Smooth  Surfaces. — If  we  let  a  ray  of 
sun-light  enter  a  darkened  room,  and  fall  upon  a  polished  metal- 
lic surface,  we  generally  notice  the  two  following  phenomena: — 
1.  We  observe  a  ray  which  seems  to  have  come  in  a  certain 
direction  from  the  mirror,  forming  a  little  image  of  the  sun 
upon  the  objects  with  which  it  comes  in  contact,  as  if  a  direct 
sunbeam  had  struck  the  spot;  such  rays  are  regularly  reflected, 
and  the  intensity  of  their  light  is  more  considerable  in  proportion 
as  the  mirror  is  well  polished.  2.  From  different  parts  of  the 
dark  room,  we  may  distinguish  that  part  of  the  mirror  which 
is  struck  by  the  incident  sunbeam;  this  arises  from  a  portion 
of  the  incident  light  being  irregularly  reflected:  that  is,  scattered 
in  all  directions  from  the  incident  sunbeam.  The  intensity  of 
the  scattered  light  is  greater  in  proportion  as  the  mirror  is  imper- 
fectly polished. 

If  there  were  absolutely  smooth  reflecting  surfaces,  we  should 
not  be  able  to  perceive  them  by  our  eyes,  for  bodies  are  only 
rendered  perceptible  from  a  distance,  by  the  rays  scattered  upon 
their  surfaces.  Regularly  reflected  rays  show  us  the  images  of 
the  luminous  point  whence  they  originate,  but  not  the  reflecting 
body.  In  a  very  good  mirror  we  scarcely  perceive  the  reflecting 
surface  intervening  between  us  and  the  images  it  shows  us. 

We  will  now  proceed  to  determine  the  direction  of  regularly 

reflected  rays.     In  Fig.  239,  if  r  i  be  the  direction  of  the  incident 

ray,  and  i  p  a  perpendicular  drawn  from  the  sur- 

Fig.  239.          face  Qf  tke  mirror .  tne  rav  wju  be  reflected  in 

such  a  direction  i  d  that  the  angle  of  reflection 
f,    d  i  p  is  equal  to  the  angle  of  incidence  r  i  p ; 
the  ray,  therefore,  makes  before  and  after  its 
reflection,  the  same  angle  with  the  perpendicular :  farther,  the 


REFLECTION   OF   LIGHT.  259 

i 

incident  ray,  the  perpendicular,  and  the  reflected  ray,  all  lie  in 
the  same  place. 

By  the  help  of  these  principles,  we  may  easily  prove  that  a 
plane  mirror  must  show  the  images  of  objects  lying  before  its 
smooth  surface,  and  that  the  images  and  object  must  be  symmer 
trical  in  relation  to  the  reflecting  plane. 

Let  m  m'  (Fig.  240)  be  a  smooth  mirror,  /  a  luminous  point  be- 
fore it,  and  throwing  a  ray  /  i  upon 

it.     This  ray  is  now  reflected  in      Fig'  240t 

the  direction  i  c,  in  accordance 
with  known  laws,  and  if  the  re- 
flected ray  impinge  upon  the  eye, 
it  will  produce  the  same  effect  as 
if  it  came  from  a  point  behind  the 
mirror,  lying  upon  the  prolongation 
of  c  i,  and  at  a  distance  from  the  eye  equal  to  the  space  the  ray 
must  really  traverse  from  /  to  i,  and  from  thence  to  the  eye  ;  we, 
therefore,  find  this  point  /',  by  prolonging  c  i,  and  making  i  V  = 
i  1.  If,  now,  we  join  I  and  V  by  a  straight  line,  we  may  easily 
show  that  the  triangles  I  i  k  and  V  i  k,  are  equal  to  one  another, 
and  thence  it  further  follows,  that  /  /'  is  at  right  angles  to  m  mf, 
and  that  /  k  =  I'  k.  In  order,  therefore,  to  find  the  image  of  a 

luminous  point  on  a  smooth  mirror,  it 

j  .     j  .    ~  „  Fig.  241. 

is  only  necessary  to  let  fall  a  perpen- 

dicular  from  the  luminous  point  on 
the  mirror,  or  on  its  prolongation,  and 
to  prolong  it  as  far  behind  the  surface 
of  the  mirror  as  the  luminous  point 
lies  before  it. 

As  this  applies  to  any  point  of  a 
body  emitting  light,  whether  that  light 
be  its  own,  or  scattered  rays,  we  may 
easily  construct  the  image  of  an  ob- 
ject. Let  V  W  be  a  plane  mirror, 
(Fig.  241,)  A  B  an  arrow  lying  before 
it:  we  shall  find  the  image  of  the 
point,  if  we  let  fall  a  perpendicular 
Ji  k  from  Ji  to  the  surface  of  the  mir- 
ror, and  make  its  prolongation  a  k 
equal  to  Ji  k ;  all  the  rays  passing  from  Ji  appear  to  diverge  after 


260  ANGLES   OF   REFLECTION. 

reflection,  as  if  they  came  from  a  ;  a  is,  therefore,  the  image  of  Ji ; 
in  the  same  way  it  follows  that  b  must  be  the  image  of  B ;  the 
appearance  of  the  figure  shows  clearly  that  both  the  image  and 
the  object  are  symmetrical  in  relation  to  the  surface  of  the 
mirror. 

The  direction  of  the  reflected  light  may,  therefore,  be  determined 
with  geometrical  exactitude ;  but  this  is  not  the  case  with  respect 
to  the  intensity  of  the  reflected  rays. 

In  general,  the  following  holds  good : 

1.  The  intensity  of  regularly  reflected  light  increases  with  the 
angle  of  incidence,  without,  however,  being  null  at  rectangular 
incidence. 

2.  It  depends  upon  the  medium  in  which  the  light  moves, 
and  against  which  it  impinges. 

We  will  here  adduce  a  few  examples  for  the  sake  of  making 
the  matter  clearer. 

If  the  rays  passing  from  the  flame  of  a  taper  fall  nearly  at  right 
angles  on  a  plate  of  ground  glass,  we  are  unable  to  distinguish  any 
image  of  the  flame,  but  perceive  it  plainly  when  the  rays  fall  upon 
the  glass  obliquely ;  in  this  case,  we  may  also  see  the  image  on 
polished  wood,  shining  colored  paper,  &c. ;  whence  it  follows,  that 
the  quantity  of  reflected  light  is  increased  in  proportion  with  the 
obliquity  of  the  rays. 

Angles  of  reflection. — If  two  mirrors  be  placed  together,  at  any 
angle,  we  see  many  images  of  the  objects  intervening  between 
them,  their  number  depending  upon  the  inclination  of  the  mirrors. 

Fig.  242. 


ANGLES    OF   REFLECTION.  261 

Let  V  W  and  Z  W,  in  Fig.  242,  be  two  plane  mirrors,  meeting  at 
right  angles;  and  A,  a  luminous  point  within  the  angle  formed  by 
them.  In  the  first  place,  an  image  of  A  will  be  seen  in  each  mirror, 
appearing  in  the  one  at  a,  and  in  the  other  at  a' ;  an  eye  at  0  will 
see,  besides  the  object ./?,  the  images  a  and  a'  reflected  from  A  by  a 
single  reflection.  But  all  rays  reflected  from  one  mirror  may  fall 
upon  the  other  mirror,  and  suffer  reflection  from  the  latter.  As 
all  the  rays  reflected  from  the  first  mirror  diverge  as  if  they  came 
from  a,  a  is,  to  some  extent,  an  object  which  sends  rays  to  the 
mirror  Z  W9  and  we  may,  consequently,  easily  find  the  reflected 
image  of  a  in  the  mirror  Z  W-,  let  us  now  let  fall  a  perpendicular 
from  a  on  the  prolongation  of  Z  W,  producing  it  in  the  manner 
already  indicated,  when  we  obtain  the  image  a",  from  which  all 
the  rays  appear  to  emanate,  which  are  reflected  from  the  mirror 
V  W  to  the  mirror  Z  W,  where  they  undergo  a  single  reflection ; 
and  thus  the  eye  at  0  perceives  another  image  at  a"  after  a  second 
reflection. 

But  the  image  a  is  an  object  for  the  mirror  V  W,  and  if  we 
determine  the  situation  of  the  image  of  a',  we  find  that  it  is  like- 
wise a" ;  that  is,  all  the  rays  reflected  from  Z  W  upon  the  mirror 
V  W,  diverge  after  the  second  reflection  as  if  they  came  from  a". 

The  rays  reflected  a  second  time  do  not  fall  upon  either  of  the 
mirrors  ;  or,  in  other  words,  no  further  image  of  a"  is  visible ;  we 
therefore  see,  besides  the  object  A  in  this  case,  three  images  of  it. 

If  the  mirrors  had  inclined  at  an  angle  of  60°,  45°,  or  36°,  that 
is,  if  the  angle  they  made  amounted  to  the  £,  |,  or  iV  of  the 
whole  circumference,  we  should  have,  inclusive  of  the  object  itself, 
6,  8,  or  10  images. 

Upon  this  principle  rests  the  construction  of  the  kaleidoscope. 

As  we  have  seen,  the  number  of  the  images  increases  if  the 
angle  be  diminished ;  their  number  becomes  infinitely  great  if  the 
angle  of  the  mirrors  be  null ;  that  is,  if  the  mirrors  be  parallel  to 
each  other. 

Reflection  from  Curved  Mirrors. — If  a  ray  of  light  fall  upon  a 
curved  surface  at  any  point,  it  will  be  reflected  exactly  as  if  it  had 
fallen  upon  the  plane  tangent  to  this  point.  A  luminous  point 
which  is  placed  in  the  centre  of  a  polished  sphere,  therefore,  will 
send  rays  of  light  to  all  points  of  the  spherical  surface,  which  will 
be  all  thrown  back  collectively  to  the  centre. 

If  we  take  a  hollow  sphere,  whose  inner  surface  is  well  polished, 


262 


CONCAVE    SPHERICAL   MIRRORS. 


Fig.  243. 


then  a  piece  cut  from  this  sphere  by  a  plane,  forms  a  concave 
spherical  mirror  ;  while  a  convex  spherical  mirror  is  a  section  of 
a  sphere  polished  externally. 

The  diameter  of  a  spherical  mirror  is  the 
line  m  m',  Fig.  243,  connecting  two  oppo- 
site points  of  the  edge ;  the  line  c  a,  con- 
necting the  middle  point  of  the  sphere  with 
the  middle  of  the  mirror,  is  termed  its  axis  ; 
and  the  angle  formed  by  the  lines  c  m  and 
c  m',  its  aperture.  The  central  point  c  of 
the  sphere,  of  which  the  mirror  is  a  part,  is  also  called  the  centre 
of  curvature. 

Of  Concave  Spherical  Mirrors. — Let  A  B,  Fig.  244,  be  the  sec- 
Fig.  244. 


tion  of  a  spherical  concave  mirror,  whose  centre  is  m.  Let  a  be 
a  luminous  point,  throwing  its  rays  upon  the  mirror.  If,  now, 
we  draw  a  straight  line  a  m  d  from  the  point  a  through  the  centre 
of  the  sphere  to  the  mirror,  this  line  will  be  the  axis  of  the  conical 
pencil  of  rays  reflected  by  the  mirror.  It  is  easy  to  find  how  a 
ray  a  b  of  this  pencil  of  rays  is  reflected  from  the  mirror,  for  the 
straight  line  drawn  from  b  to  the  focus  m  is  the  perpendicular  at 
the  point  of  incidence.  If  we  make  the  angle  i  =  to  the  angle  if, 
b  c  is  the  reflected  ray. 

If  we  suppose  a  circle  to  be  drawn  upon  the  mirror,  whose 
points  are  all  as  far  from  d  as  6,  it  is  easy  to  see  that  all  rays 
emitted  from  a,  and  striking  the  mirror  at  any  point  of  this 
circle,  are  so  reflected  that  they  cut  the  axis  a  d  in  the  same 
point  c. 

If  the  luminous  point  be  very  far  removed,  we  may  consider 
all  the  rays  it  throws  upon  the  mirror  as  parallel  to  each  other. 
Let  us  determine  the  position  of  the  point  c  for  this  case.  In  Fig. 
245  let  a  b  be  an  incident  ray  of  light  parallel  to  the  axis ;  b  m 


CONCAVE  SPHERICAL  MIRRORS.  263 

the  perpendicular  at  the  point  of  incidence  ;  then  it  is  evident  that 
i  =  x.  If,  now,  the  angles  i  and  x  are  very  small,  the  angle  b  c 
m  is  so  obtuse  that  the  sura  of  the  sides  b  c  and  c  m  is  not  much 
greater  than  the  radius  b  m,  and  since  b  c  =  c  m,  c  m  is  very 
nearly  equal  to  \  b  m, 

that  is,  almost  equal  to  Fig' 2 

half  the  radius;  we 
may  therefore  assume, 
without  any  serious 
error,  that  rays  parallel 
with  the  axis,  falling 

upon  the  mirror  in  such  points  b,  that  the  arc  b  d  embraces  but  a 
small  angle,  meet  at  one  point  of  the  axis,  lying  equi-distant  be- 
tween the  centre  of  the  mirror  and  the  mirror  itself.  Rays  lying 
so  near  the  axis  that  the  value  of  m  c  does  not  differ  materially 
from  J  m  b,  are  termed  central  rays.  The  point  of  union  of  the 
parallel  and  central  incident  rays  bears  the  name  of  the  principal 
focus.  (It  will  be  marked  F  in  the  following  figures.)  This  focus 
lies,  as  we  have  seen,  equi-distant  between  the  centre  of  the  mirror 
and  the  mirror  itself,  upon  the  axis  of  the  parallel  rays. 

Fig.  246.  Fig/  247. 


The  more  the  angle  i  increases,  that  is,  the  further  the  rays  fall 
from  the  axis  of  the  mirror,  the  greater  is  the  curvature  of  the 
mirror  from  the  point  of  incidence  to  its  centre,  and  the  more  the 
point  c,  in  which  the  reflected  rays  cut  the  axis,  approaches  the 
mirror.  The  point  of  union  of  the  rays  that  are  not  central,  lies, 
therefore,  nearer  to  the  mirror  itself  than  the  principal  focus,  as 
may  be  seen  from  Fig.  247. 

In  order  to  make  a  concave  mirror  applicable  to  optical  pur- 
poses, the  rays  emitted  from  one  point  must  re-unite  as  nearly  as 
possible  in  another  single  point.  This,  however,  is  only  possible 
if  the  aperture  of  the  mirror  be  inconsiderable,  not  exceeding,  at 
most,  8  to  10°;  for,  in  that  case,  we  may  consider  all  the  rays 


264 


CONCAVE    SPHERICAL   MIRRORS. 


falling  upon  the  mirror  as  central  rays.  We  will  confine  ourselves 
to  the  consideration  of  such  mirrors,  and,  consequently,  of  central 
rays  only. 

The  above-mentioned  fault,  that  all  rays  falling  parallel  with 
the  axis,  are  not  united  exactly  in  one  point,  is  termed  spherical 
aberration. 

If  the  luminous  point  is  not  at  an  unreasonable  distance,  but 
simply  such  a  one  that  we  cannot  neglect  the  divergency  of  the 
rays  falling  upon  the  mirror,  the  focus  will  change  its  position, 
departing  more  and  more  from  the  mirror  the  nearer  the  luminous 
point  approaches  it.  That  such  is  the  case  may  easily  be  seen 
from  Fig.  248.  The  nearer  the  luminous  point  is,  the  smaller  will 

Fig.  248. 


be  the  angle  i  to  the  same  point  b  of  the  mirror,  the  smaller,  also, 
will  be  the  angle  if,  and  the  more  c  will  move  towards  m.  If, 
therefore,  a  luminous  point  constantly  approaches  the  mirror,  from 
which  it  was  so  far  removed  that  its  rays  were  again  concentrated 
in  the  principal  focus,  the  focus  will  continue  to  recede  from 
the  principal  focus,  approaching  the  central  point,  until,  at  last, 
when  the  luminous  point  is  in  the  centre  of  the  mirror,  the  focus 
coincides  with  it.  If  the  luminous  point  approach  still  nearer  to 
the  mirror,  the  focus  falls  farther  and  farther  from  the  mirror;  and, 
if  it  arrives  at  the  principal  focus,  its  rays  will  be  reflected  from 
the  mirror  parallel  with  the  axis. 

Fig.  249  represents  the  only  remaining  case,  namely,  that  of 
the  luminous  point  s  lying  between  the 
mirror  and  the  principal  focus.  Here  the 
rays  are  so  reflected  that  they  diverge  after 
the  reflection  as  if  they  had  come  from 
a  point  v  lying  behind  the  mirror,  and 
which  may  easily  be  found  by  construction 
for  any  given  case. 

We  have  hitherto  considered  only  such 


Fig.  249. 


IMAGES    PRODUCED    BY    CONCAVE    MIRRORS. 


265 


luminous  points  as  lie  on  the  axis  of  the  mirror,  where,  conse- 
quently, the  axis  of  the  rays  thrown  upon  the  mirror  coincides 
with  the  axis  of  the  mirror  itself.  All  the  laws  we  have  hitherto 
developed  apply,  however,  equally  to  such  luminous  points  as  lie 
out  of  the  axis  of  the  mirror ;  let  A  be  such  a  luminous  point  in 
Fig.  250.  If  we  draw  a  line  from  A  through  m  to  the  mirror, 

Fig.  250. 


this  is  the  axis  of  the  conical  pencil  of  rays  cast  on  the  mirror,  and 
on  this  axis  all  the  rays  emanating  from  A  must  again  unite.  If 
a  whole  pencil  of  rays  fell  parallel  to  A  m  b  upon  the  mirror, 
they  would  re-unite  after  reflection  in  the  point  f,  lying  half  way 
between  m  and  b ;  as,  however,  the  rays  coming  from  A  diverge, 
their  point  of  re-union  will  lie  further  from  the  mirror  thany.  We 
may  easily  find  this  point  of  union  by  construction.  Let  us  draw 
a  line  A  n  from  A  parallel  with  the  axis  of  the  mirror.  A  ray 
falling  upon  the  mirror  in  this  direction  will  evidently  be  reflected 
towards  the  principal  focus  F\  if,  now,  we  draw  a  line  from  n 
through  Fj  this  line  will  cut  the  line  A  m  6,  the  point  of  intersec- 
tion a  is  clearly  that  in  which  all  the  rays  coming  from  A  are  again 
united  after  their  reflection  by  the  mirror ;  in  short,  a  is  the  image 
of  A. 

Of  the  Images  produced  by  Concave  Mirrors. — In  Fig.  251  let 

Fig.  251. 


23 


266      IMAGES  PRODUCED  BY  CONCAVE  MIRRORS. 

A  B  represent  an  object  lying  between  the  centre'  of  curvature 
C  of  the  mirror,  and  the  principal  focus  F.  From  what  has  been 
already  said,  it  is  easy  to  find  the  image  of  the  point  A  as  it  lies 
upon  the  line  drawn  through  C  and  A,  since  a  ray  A  n  is  reflected 
in  the  direction  n  A.  A  ray  A  e  falling  from  a  parallel  to  the  main 
axis  on  the  mirror,  will,  however,  be  reflected  by  the  principal 
focus  F.  The  rays  reflected  in  the  directions  n  A  and  e  F  inter- 
sect each  other  at  a,  and  here  is  the  image  of  A.  In  like  manner, 
we  can  find  the  image  b  of  the  point  B,  and  thus  we  see,  that,  by 
means  of  a  concave  mirror,  we  may  obtain  beyond  C  an  inverted 
and  enlarged  image  of  an  object  A  B  lying  between  the  principal 
focal  point  and  the  centre  of  curvature. 

As  the  rays  issuing  from  A  are  united  at  a,  so  conversely,  if  a 
were  a  luminous  point,  the  rays  issuing  from  it  would  be  reflected 
by  the  mirror  at./?;  in  short,  A  is  in  this  case  the  image  of  a, ;  in 
like  manner,  B  is  the  image  of  b.  If,  therefore,  an  object  a  b  be 
beyond  the  centre  C,  the  concave  mirror  will  give  an  inverted  and 
diminished  image  between  the  centre  C  and  the  principal  focal 
point  F. 

The  images  we  have  been  considering  are  essentially  different 
from  those  yielded  by  plane  mirrors.  All  rays  emitted  from  a 
luminous  point  are  reflected  from  a  plane  mirror  in  such  a  direc- 
tion as  if  they  came  from  a  point  behind  the  mirror,  consequently 
they  diverge.  In  the  cases  above  considered,  however,  the  rays 
issuing  from  any  point  of  the  object  are  actually  again  collected 
by  means  of  the  mirror  in  one  point ;  we  will,  therefore,  for  the 
sake  of  distinction,  call  these  images  convergent  images.  They 
may  be  received  on  a  screen  of  white  paper,  or  ground  glass,  and 
an  image  may  be  thus  obtained  exactly  resembling  the  object  in 
all  its  relations;  the  points  of  the  screen,  strongly  illuminated  by 
the  concentration  of  the  rays,  scatter  the  light  in  all  directions,  and 
the  image  is  then  still  visible  if  the  rays  reflected  from  the  mirror 
do  not  come  direct  to  the  eye. 

The  further  the  object  is  moved  from  the  concave  mirror,  the 
more  the  image  must  approach  the  principal  focal  point,  as  may 
easily  be  understood  ;  the  image  of  the  immeasurably  remote  sun 
must,  therefore,  lie  in  this  focal  point,  if  the  axis  of  the  mirror  be 
directed  towards  the  sun.  If  the  sunbeams  fall  obliquely,  and 
consequently  not  in  the  direction  of  the  axis  of  the  mirror,  the 
image  will,  of  course,  no  longer  be  in  the  axis,  but  to  the  side  of  it, 


IMAGES  PRODUCED  BY  CONCAVE  MIRRORS.      267 

its  distance  from  the  mirror  being,  however,  always  equal  to  half 
the  radius  of  curvature  of  the  latter.  As  the  sun  appears  to  us  at 
an  angle  of  about  30',  the  image  of  the  sun  seen  from  C  must 
appear  at  the  same  angle;  its  absolute  size  depending,  conse- 
quently, upon  the  radius  of  curvature  of  the  mirror.  For  instance, 
in  the  focus  of  Herschel's  large  reflector,  whose  radius  of  curva- 
ture is  50  feet,  the  sun's  image  is  about  3  inches  in  diameter; 
the  diameter  of  the  sun's  image  is  about  3  millimetres,  (0.118 
inch,)  if  the  radius  of  curvature  of  the  mirror  be  1  metre,  (39 
inches.) 

In  order  to  find  the  radius  of  curvature  of  a  concave  mirror,  we 
need  only  measure  the  distance  at  which  the  sun's  image  lies 
from  the  mirror,  since  twice  this  distance  is  equal  to  the  radius  of 
curvature  required.  The  images  of  such  objects  as  are  removed 
more  than  100  times  the  length  of  the  radius  of  curvature  from 
the  mirror  are  extremely  near  the  focus  itself. 

We  have  still  to  ascertain  the  position  of  an  image  where 
the  object  lies  between  the  mirror  and  the  focus.  We  have 
seen,  that  all  rays  emanating  from  a  luminous  point  that  is 
nearer  to  the  concave  mirror  than  is  the  principal  focal  point,  are 
reflected  as  if  they  came  from  a  point  behind  the  mirror;  in  the 
case  we  are  about  to  consider,  there  cannot,  therefore,  arise  any 
combined  convergent  image. 

Let    A  By    Fig.  Fig.  252. 

252,  be  the  object 
whose  image  we 
would  seek.  The 
ray  A  n  falling  at 
right  angles  upon 
the  mirror  is  re- 
flected in  the  direc- 
tion n  A  C,  while 
the  ray  A  e,  which 
strikes  the  mirror  in  a  direction  parallel  to  its  axis,  will  be  thrown 
back  towards  the  principal  focal  point  F\  the  rays  nA  C  and  eF 
do  not,  however,  coincide,  but  their  directions  intersect  each  other 
behind  the  mirror  at  a,  if  prolonged  sufficiently  backwards;  and 
this  point  a  is  the  image  of  A.  In  like  manner,  the  image  b  of 
the  point  B  may  be  found;  if  therefore  the  object  lie  between  the 
focus  and  the  mirror,  a  magnified  and  erect  image  will  fall  behind 


268  THE    CONVEX   MIRRORS. 

the  mirror;  it  is  therefore  precisely  the  same  as  images  of  plane 
mirrors,  with  the  exception  of  the  enlargement  of  the  image. 
Convex  mirrors  have  no  actual,  but  merely  an  imaginary,  or,  as 
it  is  commonly  termed,  a  virtual  focus; 
that  is  to  say,  the  rays  incident  upon 
them  are  not  united  at  one  point,  but 
diverge,   after   reflection,  as  if  they 
had  come  from  a  point   behind  the 
mirror.     If  rays  parallel  to  the  axis 
fall  upon   convex  mirrors,  their  ima- 
ginary focus  will  be  half  way  between 
the  mirror  and  the  centre  c.     It  is  consequently  easy  to  construct 
the  images  obtained  by  these  mirrors. 

Let  VW  be  a  convex  mirror,  Fig.  254,^25  an  object  before  it. 

A  ray  A  n  falling 

Fig- 254-  at  right  angles  to 

the  mirror  will  be 
reflected  in  the  di- 
rection nJl)  while 
the  ray  A  e,  paral- 
lel to  the  axis,  will 
be  reflected  in  the 
direction  eg,  as  if 
it  came  from  the 
vertical  principal 
focus  F.  If  we 
prolong  e  g  and 

nA  backwards,  these  will  cut  each  other  behind  the  mirror  at  a; 
here,  therefore,  is  the  image  of  A,  that  is  to  say,  all  rays  emitted 
from  A  are  reflected  by  the  convex  mirror,  as  if  they  came  from  a. 
After  we  have  found  the  image  b  of  the  point  of  B,  we  shall 
easily  perceive  that  we  obtain  in  convex  mirrors  diminished  erect 
images  behind  the  mirror. 

Of  the  Focal  Lines  or  Caustics. — Although  the  rays  of  light 
emitted  from  a  luminous  point  do  not  unite  again  in  the  same 
point  after  their  reflection  from  a  curved  surface,  every  two  adja- 
cent reflected  rays  will  always  intersect  each  other;  all  points  of 
intersection  of  two  adjacent  rays  reflected  in  the  same  plane  yield 
a  curved  line,  termed  the  focal,  or  caustic  line,  and  their  nature 
depends  upon  the  nature  of  the  reflecting  surface.  All  caustic 


THE   CONVEX   MIRRORS. 


269 


lines  produced  by  a  reflecting  curved  surface,  form,  when  taken 
collectively,  a  curved  surface  termed  a  caustic  surface.     Near  this, 
the  intensity  of  the  light  is 
the  greatest,  as  we  may  see  Fis- 255- 

by  the  heart-shaped  line 
forming  itself  within  a  cylin- 
drical vessel  or  a  ring,  when 
either  is  lighted  by  the  rays 
of  the  sun  or  of  a  flame. 
Fig.  255  shows  a  focal  line  of 
this  kind  formed  by  a  curved 
reflecting  strip  of  steel. 


270 


DIOPTRICS. 


CHAPTER   II. 


Fig.  256. 


DIOPTRICS,  OR  THE  REFRACTION  OF  LIGHT. 

BY  refraction  we  mean  the  deviation,  or  change  of  direction, 
suffered  by  a  ray  of  light  in  passing  from  one  medium  to  another. 
The  following  experiment  will  convince  us  of  the  actual  occur- 
rence of  such  a  change  in  direction. 

Let  us  lay  a  piece  of  money,  or  a  piece  of  metal,  ra,  at  the  bot- 
tom of  a  vessel  v  vf,  Fig.  256, 
and  direct  the  eye  o  in  such  a 
manner  as  to  see  merely  the 
edge  of  the  object,  while  the 
rest  of  it  appears  covered  by 
the  rim  b  of  the  vessel.  If, 
now,  water  be  poured  into  the 
vessel,  the  piece  of  money  will 
appear  to  rise  more  and  more, 
and  as  the  level  of  the  water  rises  in  the  vessel,  the  whole  piece 
of  money  will  at  last  become  visible,  appearing  to  lie  at  n, 
although,  in  the  meantime,  neither  the  object  nor  the  eye  has 
changed  its  position.  The  light  no  longer  comes  in  a  straight 
line  from  m  to  o,  but  describes  the  broken  line  m  i  o. 

The  angle  of  incidence  in  refraction,  as  in  reflection,  is  the  angle 
which  the  incident  ray  /  i,  Fig.  257,  makes  with  the  perpendicular 
i  n  let  fall  at  the  point  of  incidence. 

The  angle  of  refraction  is  that  angle  made 
by  the  refracted  ray  i  r  with  the  prolongation 
i  nf  of  the  perpendicular  at  the  point  of  in- 
cidence. 

The  plane  of  incidence  is  that  which  passes 
through  the  incident  ray,  and  the  perpendi- 
cular at  the  point  of  incidence  ;  the  plane  of  refraction  passes 
through  the  refracted  ray  and  the  above  perpendicular. 


THE   PLANE   OF   INCIDENCE. 


271 


Fis-  258- 


The  plane  of  refraction  corresponds  with  the  plane  of  incidence, 
but  the  following  relations  exist  between  the  angle  of  incidence 
and  the  angle  of  refraction. 

Let  I  b,  Fig.  258,  be  a  ray  of  light  falling  upon  a  surface  of 
water,  and  bf  the  corresponding  re- 
fracted ray.  If  we  now  suppose  a 
circle  to  be  drawrn  around  6,  it  will 
intersect  the  incident  ray  at  a,  and 
the  refracted  ray  at  f  ;  and  letting 
fall  a  perpendicular  a  d  from  «,  and 
anothery  df  fromy,  on  the  perpendi- 
cular at  the  point  of  incidence,  then 
f  d  will  be  f  of  a  d. 

The  same  relation  always  exists  in 
the  passage  of  a  ray  of  light  from 
the  air  into  water  between  the  direc- 
tion of  the  incident  and  the  refracted 
ray.  If,  in  Fig.  259,  the  incident  ray 
/  c  were  refracted  towards  c  r',  I  c 
towards  c  r,  and  /"  c  towards  c  r", 
then  r"/'  =  f  I"  df,rf=$ld  and 


Fig.  259. 


If  the  radius  of  the  circle,  Fig. 
259,  be  =  1,  we  call  the  above 
mentioned  perpendicular  the  sine  of  the  corresponding  angle  ;  I'  d' 
is  the  sine  of  the  angle  /'  c  p  ;  /  d  =  sin.  I  c  p  ;  I"  d"  =  sin. 
V  c  p',  in  the  same  manner  r'f=  sin.  r*  c  p1  ;  rf=  sin.  r  cp1; 
ij'f'  =  sin.r"cpf. 

By  the  introduction  of  this  designation,  the  law  of  refraction  for 
the  passage  of  rays  of  light  from  air  to  water  may  be  simply  ex- 
pressed as  follows  : 

The  sine  of  the  angle  of  refraction  is  always  f  of  the  sine  of 
the  corresponding  angle  of  incidence. 

In  their  passage  from  the  air  to  glass,  rays  of  light  undergo  a 
more  decided  deviation  ;  for  in  this  case  the  sine  of  the  angle 
of  refraction  is  about  f  of  the  sine  of  the  angle  of  incidence. 

The  relation  in  which  the  sine  of  the  angle  of  refraction  stands 
to  the  sine  of  the  angle  of  incidence  is  for  every  substance  dif- 
ferent ;  this  relation  is  designated  by  the  term  of  the  index,  or 


272  REFRACTION    OF    LIGHT    IN   PRISMS. 

exponent  of  refraction.     The  value  of  the  index  of  refraction  is 
for: 

Water  .     4 

Glass  .         .         .     | 

Diamond     .         .  f 

In  the  transition  of  light  from  the  air  to  the  diamond,  the  sine 
of  the  angle  of  incidence  is  consequently  2J  times  greater  than 
the  sine  of  the  angle  of  refraction  ;  in  the  diamond,  therefore,  the 
rays  of  light  suffer  a  very  considerable  deviation.  The  diamond 
is  a  highly  refracting  substance. 

Refraction  of  Light  in  Prisms. — A  prism  is  a  term  applied  in 
optics  to  a  transparent  medium,  bounded  by  two  surfaces  inclining 
towards  each  other. 

The  edge  of  the  prism  is  the  line  in  which  the  two  bounding 
surfaces  intersect,  or  would  intersect  each  other,  if  they  were 
sufficiently  extended. 

The  base  of  a  prism  is  any  one  of  the  surfaces  opposite  to  one 
of  the  refracting  edges,  whether  it  actually  exist  or  is  only  ima- 
ginary. 

The  refracting  angle  is  the  angle  made  by  the  two  surfaces  of 
the  prism. 

The  principal  section  is  the  section  of  the  prism  by  a  plane  at 
right  angles  to  one  of  its  edges. 

The  prisms  generally  made  use  of,  are 
such  as  are  bounded  by  rectangular  surfaces 
a  b  a'  br,  b  c  V  d ,  and  c  a  c1  a.  If  light 
pass  through  the  surfaces  a  br  and  a  c7,  a  a! 
is  the  refracting  edge,  and  the  surface  b  cf 
the  base ;  b  V  is  the  refracting  edge  if  the 
Fig.  261.  ray  of  ijght  pass  the  surface  b  a'  and  b  c1 . 

The  principal  section  of  such  a  prism  is  a  triangle, 
and  according  as  this  latter  is  rectangular,  isosceles  or 
equilateral,  the  prism  is  rectangular,  isosceles,  or  equi- 
lateral. 

The  prisms  are  usually  fastened  to  a  brass  stand 
(Fig.  261.) 

By  pushing  the  rod  t  up  or  down  the  tube  in  which 
it  is  inserted,  the  prism  may  be  raised  or  lowered,  and 
by  means  of  the  joint  at  g  it  may  be  inclined  in  any 
direction. 


REFRACTION   OF    LIGHT   IN   PRISMS. 


273 


If  we  hold  a  prism  in  such  a  manner  that  the  refracting  edge 
is  directed  upwards,  we  observe  on  looking  through  it  two  re- 
markable phenomena:  in  the  first  place,  all  objects  appear  to  be 
considerably  displaced  from  the  position  they  actually  occupy, 
and  so  much  raised  that  the  eye  at  o  (Fig.  262)  sees  the  object  a 
through  the  prism  at  a' ;  and  Fig.  262. 

secondly,  they  appear  to  have  _a/ 

colored  edges.    If  the  refracting  .,.-••'"" 

edge  were  directed  downwards, 
all  objects  seen  through  the  prism 
would  seem  to  be  removed  down- 
wards out  of  their  right  place. 
A  vertical  prism  displaces  objects  to  the  right  or  left,  according 
to  the  side  to  which  the  refracting  edge  is  turned. 

By  altering  the  experiments  in  this  manner,  we  shall  easily  be 
convinced  that  all  objects  seen  through  the  prism  appear  removed 
towards  the  direction  of  the  refracting  edge. 

If  a  ray  of  sun-light  enter  a  dark  room  through  a  small  open- 
ing in  the  direction  v  d,  and  be  received  upon  a  prism,  we  shall 
observe  a  deviation  and  a  coloring.  If  the  prism  is  in  a  hori- 
zontal position,  and  its  refracting  edge  turned  upward,  instead  of 
the  white  round  image  of  the  sun, 
which  would  appear  without  the  prism 
at  d,  we  perceive  an  oval  image  co- 
lored with  the  hues  of  the  rainbow,  the 
solar  spectrum,  at  r.  If  the  refracting 
margin  were  directed  downwards,  the 
prismatic  solar  image  would  appear 
above  d.  By  a  vertical  prism,  the 
sun's  image  would  deviate  to  the  right 
or  left  according  to  the  position  of  the  former. 

These  phenomena  of  color  will  be  subsequently  considered ;  we 
shall,  at  present,  only  speak  of  the  deviation. 

The  above-mentioned  phenomena  admit  of  easy  explanation. 
Let  a  s  (Fig.  264)  be  the  first,  and  a'  s  the 
second  surface  of  a  glass  prism ;  /  i  the 
incident,  i  i'  the  refracted,  and  i'  e  the 
emergent  ray.  On  its  passage  from  the 
air  into  the  glass,  the  incident  ray  is  re- 
fracted, and  brought  nearer  to  the  perpen- 


Fig.  263. 


Fig.  264. 


274 


REFRACTION   OF   LIGHT   BY   LENSES. 


dicular  at  the  point  of  incidence  i  n ;  having  reached  the  second 
surface,  it  is  again  refracted,  but  removed  further  from  the  per- 
pendicular i'  n'  on  its  transition  into  the  air. 

A  prism  will,  other  circumstances  being  the  same,  cause  rays 
of  light  to  deviate  in  proportion  to  the  magnitude  of  the  refracting 
angle.  If  this  angle  be  60°,  the  deviation  will  be  more  conside- 
rable than  with  one  of  only  45°. 

A  prism,  consisting  of  a  strongly  refracting  substance,  causes 
the  rays  of  light  to  deviate  more  considerably  than  a  like- 
shaped  prism  of  a  less  powerfully  refracting  substance.  In  a 
prism  of  water,  the  deviation  is  less  considerable  than  in  one  of 
glass. 

In  the  same  prism,  the  amount  of  deviation  varies  according 
to  the  direction  in  which  the  rays  of  light  are  incident  upon  the 
first  surface. 

On  looking  at  an  object  through  a  prism,  we  see  how  the  image 
removes  further  from  the  position  of  the  object,  and  then  again 
draws  nearer  to  it  as  we  turn  the  prism  on  its  axis.  The  smallest 
deviation  occurs  in  the  case  where  the  rays  traverse  the  prism 
symmetrically,  as  seen  in  Fig.  264.  If  the  direction  of  the  inci- 
dent ray  were  changed  to  one  side  or  the  other,  the  deviation 
would  increase. 

In  order  to  make  prisms  of  liquids,  hollow  prisms  are  used, 
having  their  lateral  sides  formed  of  glass  plates. 

Refraction  of  Light  by  Lenses. — The  term  lens  is  applied  to  trans- 
parent bodies,  possessing  the  property  of  increasing  or  diminish- 
ing the  convergency  of  the  rays  that  pass  through  them. 

We  shall,  here,  only  treat  of  spherical 
lenses,  that  is,  such  as  have  their  bound- 
ing surfaces  composed  merely  of  por- 
tions of  spherical  surfaces  and  planes, 
since  these  alone  are  applied  to  optical 
instruments.  There  are,  also,  elliptical, 
parabolic,  cylindrical,  and  other  lenses, 
exhibiting  phenomena  similar  to  the 
spherical. 

There  are  six  different  kinds  of  lenses, 
sections  of  which  are  represented  at  Fig. 
265.     a  is  a  bi-convex  lens,  the  one  that 
bounded  by  two   externally  convex 


Fig.  265. 


IS 


REFRACTION   OF    LIGHT   BY   LENSES. 


275 


spherical  surfaces.     The  plane-convex  lens  b  is  bounded  by  one 
plane  and  one  convex  surface. 

The  concave-convex  lenses,  bounded  by  one  convex  and  one 
concave  surface,  as  c  andjf,  are  also  termed  Meniscus  lenses;  they 
are  divided  into  two  kinds,  according  as  the  degree  of  curvature  of 
the  concave  surface  is  the  lesser  of  the  two,  as  at  c,  or  the  greater 
as  at  f.  d  represents  a  bi-concave  lens,  e  one  that  is  plano- 
concave. 

The  three  former,  a,  b,  and  c,  are  thicker  at  the  centre  than  at 
the  edges,  and  are  termed  convergent  lenses.  The  three  latter, 
d,  e,  andjf,  which  are  thinner  in  the  middle  than  at  the  edges,  are 
termed  divergent  lenses. 

The  axis  of  a  lens  is  the  straight  line,  uniting  the  centre  of 
both  the  spherical  surfaces,  by  which  the  lens  is  formed.  In 
plano-concave  and  plano-convex  lenses,  the  axis  is  the  perpendi- 
cular passing  from  the  centre  of  curvature  to  the  plane. 

In  order  to  develope  the  most  important  propositions  concern- 
ing the  refraction  of  light  by  lenses,  we  must  once  more  return  to 
prisms,  and  consider  more  attentively  the  case  where  the  refract- 
ing angle  of  the  prism  is  very  small. 

In  a  prism  of  small  refracting  angle,  as  in  Fig.  266,  the  devia- 
tions may,  without  any  serious  error,  be  considered  proportional 
to  the  refracting  angle.     A  prism,  whose  re- 
fracting  angle  is  twice  as  great  as  that  in 
Fig.  266,  would  produce  twice  as  much  de- 
viation ;  and  if  the  angle  were  only  half  the 
size  of  the  one  in  Fig.  266,  the  deviation 
would  only  be  half  as  great. 

In  Fig.  267,  a  b  c  d  is  an  elongated  rhomb,  to  which  is  joined 
above,  a  parallel  trapezium  a  b  gf,  and  below,  a  like  figure  ;  the 
triangle  /  g  h  is,  there-  Fig.  267. 

fore,  found  above,  and 
one  precisely  like  it  be- 
low. The  two  sides  of 
the  parallel  trapezium, 
which  are  not  parallel  to 
each  other,  form,  when 
prolonged,  the  isosceles  triangle  with  an  angle  at  the  apex,  which 
must  be  half  as  large  as  the  angle  at  the  apex  of  the  upper  tri- 
angle at  h. 


276  REFRACTION    OF    LIGHT    BY   PRISMS. 

If  we  suppose  the  whole  figure  turned  round  the  axis  M N, 
there  will  arise  a  lens-like  body,  composed  of  many  zones.  The 
middle  of  this  will  be  a  plane  disc. 

If  now,  rays  of  light  coming  from  one  point  of  the  axis  MN 
meet  this  zone-system,  we  may  determine  the  deviation  suffered 
by  the  rays  of  light  in  each  of  these  zones,  according  to  the  laws 
of  the  refraction  of  light  in  prisms. 

Let  the  point  S  lie  so  that  a  ray  of  light  coming  from  it,  and 
meeting  the  surface  a  g  in  i,  may  experience  the  minimum  of 
deviation  in  its  passage  through  abgf,  then  the  emergent  ray 
will  be  symmetrical  with  the  incident  ray,  intersecting  the  axis 
at  a  point  R,  as  far  from  the  lens  as  S. 

A  ray  of  light  undergoing  the  minimum  of  deviation  in  the 
triangle  hfg,  is  turned  twice  as  far  from  its  original  direction 
as  infga  d,  because  the  refracting  angle  of  the  upper  prism  is 
twice  as  large  as  that  of  the  lower  one.  Such  a  ray  of  light, 
suffering  the  minimum  of  deviation  in  the  upper  triangle,  passes 
through  the  latter  in  the  direction  /  m,  which  is  parallel  to  the 
axis  JtfJV;  the  incident  ray  as  well  as  the  emergent  one  will, 
however,  necessarily  make  twice  as  large  an  angle  as  the  incident 
and  emergent  rays  corresponding  to  the  minimum  of  deviation  in 
a  bfg;  if,  therefore,  a  ray  So  pass  from  S,  making  twice  as 
large  an  angle  with  M  N  at  S  i,  it  will  be  at  the  minimum  of 
deviation  in  f  g  h,  and,  going  symmetrically  from  the  other  side, 
will  be  refracted  towards  R.  The  ray  S  I  m  R  passes  through  the 
lens  at  twice  the  distance  from  the  axis  as  the  ray'tfi  k  JR,  which 
undergoes  only  half  as  great  a  degree  of  deviation. 

If  we  suppose  the  broken  lines  d  bfh  and  c  a  g  h  of  the  former 
figures  to  be  replaced  by  circular  arcs,  whose  centres  lie  upon 
the  axis  M  JV,  we  shall  have  a  regular  lens,  Fig.  267,  instead  of 
the  lens-like  body  we  have  been  considering,  and  a  ray  of  light 
falling  upon  the  lens  at  any  spot,  as  at  a,  will  be  refracted  exactly 
as  if  it  had  fallen  upon  a  prism,  whose  diagonal  section  we  ob- 
tain by  drawing  tangents  to  the  circular  arcs  at  a  and  the  points 
opposite. 

If  we  were  to  draw  tangents  on  both  sides  from  a  second  point 
6,  twice  as  far  from  the  axis  as  a  is,  these  tangents  would  intersect 
each  other  at  an  angle  twice  as  large  as  the  angle  at  which  the 
tangents  drawn  from  a  intersect  each  other.  If  now  a  ray  of 
light  pass  through  the  lens  a  parallel  to  the  axis,  it  will  make 


REFRACTION   OF    LIGHT    BY   PRISMS.  277 

equal  angles  with  the  axis  on  its  entrance,  and  after  its  leaving 
the  lens,  intersecting  the  axis  at  the  points  S  and  R,  which  are 
equidistant  on  either  side  from  the  lens.  If,  now,  a  second  ray 
of  light  pass  from  S, 

meeting  the  lens  at  6,  it  Fis-  268- 

will  experience  twice  as 
great  a  deviation  as  at  a, 
and  on  that  account  will 
likewise  be  refracted  to- 
wards R.     A  ray  of  light 
passing  from  S,  and  fall- 
ing upon  the  lens  at  c,  which  is  three  times  as  far  from  the  axis  as 
a,  will  experience  three  times  the  amount  of  deviation  that  the 
rays  incident  at  a  undergo,  and  which  are,  therefore,  refracted 
towards  the  same  point  R. 

What  has  been  said  of  a,  b  and  c  applies  equally  to  the  inter- 
vening points ;  in  such  a  lens  as  is  represented  at  Fig.  268,  there 
is  a  point  S  upon  the  axis,  having  the  property  that  all  rays  com- 
ing from  it  and  meeting  the  lens  are  concentrated  by  the  latter  in 
one  and  the  same  point  R,  which  lies  as  far  from  the  lens  on  the 
other  side  as  S. 

These  statements  apply,  however,  only  where  the  curvature  of 
the  lens  from  the  centre  towards  the  edges  is  inconsiderable,  for 
in  that  case  only  is  the  inclination  of  the  tangents  proportionate 
to  the  distance  of  these  points  of  contact  from  the  axis.  In  the 
lenses  of  which  we  are  now  about  to  speak,  the  curvature  from 
the  middle  towards  the  edges  is  inconsiderable. 

As  long  as  the  angle  at  which  the  incident  ray  falls  upon  a 
prism  of  small  refracting  angle,  it  does  not  deviate  much  from  a 
right  angle ;  so  long,  therefore,  as  the  rays  meet  the  prisms  nearly 
in  the  direction  corresponding  to  the  minimum  of  deviation,  the 
deviation  produced  by  the  prism  will  not  differ  materially  from  the 
minimum  degree. 

This  likewise  applies  to  lenses.  If  the  lens,  Fig.  268,  meet 
a  ray  of  light  at  c,  the  direction  of  which  does  not  deviate  to 
any  great  extent  from  the  direction  Sc,  the  deviation  experienced 
by  refraction  in  the  lens  will  be  the  same  as  that  experienced  by 
the  ray  S  c. 

In  Fig.  269,  let  S  be  that  point  of  the  axis  M  JV,  whose  rays, 
meeting  the  lens,  traverse  it  symmetrically  and  are  united  on  the 
24 


278 


REFRACTION    OF    LIGHT    BY    PRISMS. 
Fig.  269. 


other  side  in  a  point  R  as  far  distant  from  the  lens  as  S.  The 
ray  S  c,  which  falls  upon  the  lens  near  its  margin,  is  refracted  in 
the  direction  c  R,  the  incident  and  the  refracting  ray  making  the 
angle  S  c  R. 

If,  now,  a  ray  of  light  coming  from  T  instead  of  S,  fall  upon  the 
lens  at  a,  the  ray  T  c  would,  from  what  has  been  said,  experience 
as  great  a  deviation  as  S  c;  we  should,  therefore,  ascertain  the 
direction  of  the  ray  after  its  leaving  the  lens,  by  drawing  the 
line  c  T  in  such  a  manner  that  the  angle  T  c  T  should  be  equal 
to  the  angle  S  c  R ;  or,  in  other  words,  we  must  make  with  c  R 
an  angle  R  c  T,  which  shall  be  equal  to  the  angle  formed  by  T  c 
and  S  c. 

But  the  ray  T  d  proceeding  from  T,  is  refracted  after  leaving 
that  point  of  the  axis,  and  falls  upon  the  lower  border  of  the  lens ; 
in  fact,  all  rays  coming  from  T7,  falling  upon  the  lens,  meet  at  T , 
for,  in  the  same  proportion  in  which  the  incident  rays  approach 
the  axis,  they  deviate  less,  and  hence  unite  together  in  T ;  so 
long,  at  any  rate,  as  the  angle  which  the  external  incident  rays 
make  with  the  axis  does  not  exceed  certain  bounds,  (that  is  to 
say,  does  not  become  so  large  that  we  can  no  longer,  without 
marked  error,  consider  the  angles  proportional  to  their  tangents.) 
If,  therefore,  the  luminous  point  approach  the  lens  from  S,  the 
point  of  union  of  the  rays  will  recede  further  from  the  lens  to 
the  other  side;  the  more  T  approaches,  the  further  T  will  recede; 
the  latter  recedes  much  more  rapidly,  however,  than  the  former 
approaches. 

Let  us  now  examine  how  rays  coming  from  a  point  F  of  the 
axis  are  refracted  by  the  lens,  Fig.  270 — F  being  so  situated  that 
F  c  =  F  S.  In  this  case,  the  angle  o  =  y  =  z.  But  now  the  ray 

F  c  is  so  refracted  by 
the  lens,  that  the  angle 
x  made  by  the  emerg- 


Fig.  270. 


ent  ray  with 
equal    to     y\ 


c  R,  is 

conse- 


FOCAL   DISTANCE.  279 

quently  x  =  z,  and  hence  it  follows  that  the  ray  F  c  is  so  re- 
fracted by  the  lens,  that  it  runs  parallel  to  the  axis. 

The  same  applies  to  all  the  other  rays,  coming  from  F,  and 
falling  upon  the  lens.  They  come  out  as  a  pencil  of  rays  parallel 
with  the  axis. 

If,  as  can  be  done  in  most  cases,  we  disregard  the  thickness  of 
the  lens  with  respect  to  the  distances  of  the  points  S  and  F  from 
it,  we  may  say,  that  the  point  F  lies  in  the  centre  between  S  and 
the  lens. 

If,  therefore,  a  luminous  point  from  £  beyond  the  lens  be  brought 
nearer  to  the  latter,  the  point  of  union  on  the  other  side  of  the 
lens  will  recede,  and  if  the  luminous  point  advance  to  JP,  the 
point  of  union  will  be  indefinitely  distant;  the  rays  emerging 
parallel  with  the  axis. 

But  if,  conversely,  rays  fall  upon  the  lens  from  a  point  lying  at 
an  indefinite  distance  upon  the  axis,  or,  in  other  words,  if  a  pen- 
cil of  rays  parallel  with  the  axis,  falls  upon  the  lens,  they  are 
united  by  the  lens  at  F.  This  point  of  union  F  of  incident  rays 
parallel  with  the  axis,  is  named  the  principal  focal  point. 

If  the  luminous  point  approach  towards  the  lens  from  this  in- 
definite distance,  the  point  of  union  will  recede  on  the  other  side 
of  the  lens ;  if  the  luminous  point  be  at  Tf,  Fig.  269,  the  point 
of  union  will  be  at  T\  if  the  luminous  point  approach  as  near  as 
JR,  the  point  of  union  will  be  at  S',  if  it  approach  so  near  to  the 
lens  as  to  stand  midway  between  it  and  -R,  that  is  to  say,  if  it 
approach  to  the  focal  distance,  the  rays  will  be  parallel  with  the 
axis  after  their  passage  through  the  lens. 

The  Focal  distance,  that  is,  the  distance  of  the  focal  point  F, 
from  the  lens,  depends  not  only  on  the  form  of  the  latter,  but 
also  on  the  index  of  the  refraction  of  the  substance  of  which  it 
is  composed. 

In  a  biconvex  glass  lens,  both  of  whose  surfaces  have  an  equal 
radius,  the  focal  points  coincide  on  both  sides  with  the  central 
points  of  the  spherical  segments,  provided  the  index  of  refraction 
of  the  glass  be  exactly  f . 

If  this  index  of  refraction  be  greater,  the  focal  point  of  the  lens 
will  be  nearer ;  but  if  it  be  smaller,  it  will  be  further  removed 
from  it. 

What  has  been  said  of  biconvex  lenses,  applies  also  to  convex 
meniscus,  and  plano-convex  glasses ;  that  is,  they  have  a  principal 


280  FOCAL    DISTANCE. 

focal  point,  in  which  are  concentrated  all  the  incident  rays  paral- 
lel with  the  axis ;  the  rays  coming  from  one  of  the  points  lying 
upon  the  axis,  and  removed  from  the  glass  about  twice  the  focal 
distance,  are  united  on  the  other  side  at  a  point  likewise  twice  the 
length  of  the  focal  distance  from  the  glass. 

In  a  plano-convex  lens  whose  index  of  refraction  is  f ,  the 
focal  point  is  twice  the  radius  of  the  curved  surface  from  the 
lens. 

If  the  luminous  point  L,  Fig.  271,  approach  so  near  the  lens 
as  to  lie  within  the  focal  distance,  the  cone  of  rays  striking  the 
lens,  is  so  strongly  divergent,  that  the  lens  is  no  longer  able  to  make 

Fig.  271. 


the  rays  converge,  or  even  merge  parallel ;  they  diverge,  how- 
ever, less  after,  than  before  their  passage  through  the  lens,  dis- 
persing as  much  as  if  they  came  from  a  point  0,  which  is  further 
removed  from  the  glass  than  the  luminous  point. 

Similar  observations  may  be  made  respecting  concave  glasses. 
If  the  incident  rays  be  parallel,  the  rays  will  diverge  in  such  a 
manner  as  if  they  issued  from  the  focal  point  of  divergence  F, 
Fig.  272 ;  if,  however,  the  luminous  point  draw  nearer,  and  the 

incident  rays  are  con- 

Fig>  272> sequently     divergent, 

this  divergence  is 
greater  after  their  pas- 
sage through  the  glass 
than  was  the  case  with 
the  parallel  incident 
rays;  the  nearer  the 
luminous  point  is  to 

the  lens,  the  nearer  the  point  of  divergence,  or  focus,  therefore, 
approaches  to  the  glass. 

We  have  still  to  consider  the  case  in  which  the  incident  rays 
are  convergent.  If  the  incident  rays  converge  towards  the  focus 
F  on  the  other  side  of  the  glass,  the  refracted  rays  emerging  from 
the  lens  are  occasionally  parallel  to  each  other,  this  being  the 


SECONDARY   AXES. 


281 


converse  of  what  is  represented  in  Fig.  272.  If  the  incident 
rays  converge  more  strongly,  they  will  still  converge  after  being 
refracted ;  but  if  the  incident  rays  converge  towards  a  point  t, 
Fig.  273,  lying  at  a  greater  distance  from  the  glass  than  the  chief 
focal  point,  they  will  still  diverge  as  if  they  came  from  a  point 
before  the  glass,  as  seen  in  the  figure.  The  consideration  of  this 

Fig.  273. 


last  case  is  important  to  the  right  understanding  of  Galileo's  tele- 
scope, of  which  we  purpose  shortly  to  speak. 

Secondary  axes. — Hitherto  we  have  only  considered  those  lumi- 
nous points  that  lie  on  the  axis  of  the  lens ;  it  now  remains  to 
show  that  what  has  been  said  applies  also  to  points  not  lying 
in  the  main  axis,  provided  that  the  secondary  axes  make  only  a 
small  angle  with  the  main  axis.  By  the  term  secondary  axis,  we 
designate  the  line  we  may  imagine  to  be  drawn  from  a  point,  not 
lying  on  the  main  axis,  through  the  middle  of  the  lens. 

Let  H,  Fig.  274,  be  a  luminous  point  not  situated  upon  the 
main  axis ;  then  all  the  rays  of  light  issuing  from  it  will  be  united 

Fig.  274. 


in  a  point  ff,  lying  in  the  secondary  axis  M  Nf,  and  as  far  re- 
moved from  the  lens  as  the  point  of  union  T  of  the  rays  issuing 
from  a  point  T9  which  lies  upon  the  main-axis,  and  is  as  far  re- 
moved from  the  lens  as  H. 

This  is  easily  proved.  The  central  ray  H  Mf  passes  unbroken 
through  the  lens;  further,  H c  =  T c  and  the  angle  c  TM=  c 
H  M'  (if  not  exactly,  still  very  nearly  so) ;  and  since  the  ray  7  c 
diverges  as  strongly  at  c  as  He,  therefore  the  angle  He  H  — 

24* 


282  IMAGES    PRODUCED    BY    LENSES. 

T  c  T  ;  consequently  the  triangle  H  c  H  =  to  the  triangle  T  c 
T,  and  thus  T  T  =  H  H  ;  H  is  therefore  as  far  removed  from 
the  lens  as  T. 

The  same  result  is  obtained  by  a  comparison  of  the  triangles 
Id  T  audHdH'. 

The  field  of  a  lens  is  the  angle  which  two  of  the  secondary  axes 
make  together;  this  definition  will  not  materially  affect  the  cor- 
rectness of  our  proofs. 

Of  the  Images  produced  by  Lenses. — Let  Jl  B,  Fig.  275,  be  an 
object  on  one  side  of  the  lens  V  W9  but  further  removed  from  it 

Fig.  275. 


than  the  focal  point  F.  The  rays  emitted  from  A  are  united  at  a 
point  a  upon  the  secondary  axis  drawn  from  «#  through  the  mid- 
dle 0  of  the  lens ;  a  is  therefore  the  image  of  */?,  and  b  is  the  image 
of  B,  consequently  a  b  is  also  the  image  of  the  object  A  B;  the 
image  is  in  this  case  inverted,  and  is  a  true  convergent  image. 

Seen  from  the  middle  of  the  lens,  the  image  and  object  appear 
at  the  same  angle,  for  the  angle  b  o  a  is  equal  to  the  angle  B  o  A, 
being  angles  at  the  vertex ;  the  greater  size  of  the  image  or  of  the 
object  depends  upon  which  of  the  two  is  furthest  removed  from 
the  glass.  If  we  assume  that  the  object  lie  twice  as  far  as  the 
focal  distance  from  the  glass,  the  image  will  be  formed  on  the 
other  side  at  an  equal  distance;  in  this  case,  therefore,  the  image 
and  the  object  are  equal  in  size.  If  the  object  approach  nearer  to 
the  glass,  the  image  will  recede,  becoming,  consequently,  larger. 
We  therefore  obtain  inverted  enlarged  images  of  objects  stand- 
ing further  from  the  glass  than  the  focal  distance,  yet  not  as  far 


IMAGES    PRODUCED    BY    LENSES.  283 

as  twice  that  distance ;  thus  the  image  a  b  in  our  figure  is  larger 
than  the  object  A  B. 

If  the  object  be  further  removed  from  the  glass  than  twice  the 
focal  distance,  the  image  will  be  nearer;  we  therefore  obtain 
inverted  diminished  images  of  distant  objects.  If,  for  instance, 
a  b9  Fig.  275,  were  an  object  lying  more  than  twice  the  focal 
distance  from  the  glass,  we  should  have  the  diminished  image 
AB. 

If  we  term  the  size  of  the  object  g,  that  of  the  image  g7,  the 
distance  of  the  object  from  the  glass  5,  and  the  distance  of  the 
image  m,  we  have 

g  :  g'  =  b  :  m, 

that  is,  the  image  and  object  are  to  one  another  as  their  distances 
from  the  lens. 

In  a  lens  of  short  focal  distance,  the  images  lie  nearer  to  the 
glass  than  in  one  of  greater  focal  distance ;  lenses  give  images, 
therefore,  small  in  proportion  to  the  shortness  of  the  focal  distance ; 
and,  conversely,  lenses  give  enlarged  images  of  small  objects 
lying  near  their  focal  point ;  at  an  equal  distance  from  the  lens, 
the  images  will  be  larger  in  such  lenses  as  have  a  small  focal 
distance,  because  in  that  case  the  object  approaches  nearer  to  the 
lens. 

If  the  object  be  within  the  focal  distance  of  the  lens,  no  con- 
vergent image  of  Ji  can  be  formed,  because  the  rays  emitted  from 
a  luminous  point,  which  lies  nearer  to  the  glass  than  does  the  focus, 
still  diverge  after  their  passage  through  it.  Let  Ji  JB,  in  Fig.  276, 
be  an  object  lying  within  this  focal  distance ;  then  the  rays  pass- 
ing from  A  will  diverge  after  emerging  from  the  glass  as  if  they 

Fig.  276. 


284  IMAGES  PRODUCED  BY  LENSES. 

came  from  a.  We  may  easily  find  the  distance  of  the  point  a 
from  the  glass  by  the  constructions  already  given.  The  rays 
coming  from  B  diverge,  after  their  passage  through  the  glass,  as  if 
they  came  from  b ;  if,  now,  there  be  an  eye  at  the  other  side  of  the 
glass,  it  will  receive  the  rays  of  light  issuing  from  the  object  Jl  B 
in  the  same  manner  as  if  they  had  proceeded  from  a  6;  a  b  is, 
therefore,  the  image  of  Jl  B.  As  the  object  and  image  both  lie 
within  the  same  angle  a  o  6,  but  the  former  is  nearer  to  the  glass, 
the  image  is  evidently,  in  this  case,  larger  than  the  object.  If 
we  use  a  lens  as  a  microscope  to  observe  small  objects,  the  en- 
larged image  seen,  is  of  the  kind  described.  We  shall  subse- 
quently revert  to  this  subject. 

Concave  glasses  do  not  give  convergent  images,  but  only  such 

as   arise   from   convex   lenses 

Flg>  277' when  the   object    lies   within 

the  focal  distance.  As  a  con- 
cave lens  causes  the  rays 
emitted  from  a  point  to  diverge 
as  if  they  came  from  a  point 
lying  nearer  to  the  glass,  it  is 
evident  that  concave  glasses 
yield  diminished  images  of  objects,  as  we  may  easily  see  from 
Fig.  277,  where  A  B  is  the  object,  and  p  q  the  image. 


DECOMPOSITION   OF    WHITE   LIGHT. 


285 


CHAPTER  III. 


Fig.  278. 


Fig.  279. 


DECOMPOSITION  OF  WHITE  LIGHT. 

White  Solar  Light  is  composed  of  different  colored  rays. — To 
prove  this,  we  need  only  form  a  solar  spectrum  in  the  manner 
already  indicated.  In  Fig.  278,  let  m  be  a  mirror,  which,  placed 
before  the  shutter  of  a 
darkened  room,  throws 
the  rays  of  the  sun  into 
it  through  the  opening 
o;  p  is  the  refracting 
prism,  and  t  a  wall  on 
which  the  images  are 
thrown.  Before  apply- 
ing the  prism,  we  see 
a  white,  round  image  at  g,  but  through  the  prism  we  obtain 
an  elongated  colored  image  r  u.  Fig.  279  exhibits  the  appear- 
ance observed  upon  the  wall  t. 

This  colored,  elongated,  solar  image  is  called  the  spectrum. 

The  length  of  this  spectrum  increases,  cteteris  paribus,  in  pro- 
portion to  the  refracting  angle  of  the  prism.  It  also  depends  upon 
the  substance  of  which  the  prism  is  formed. 

By  the  illustration  given  at  Fig.  278,  we  shall  easily  see  that 
a  white  band  is  formed  in  the  middle  of  the  spectrum,  provided 
its  length  is,  at  least,  not  twice  as  great  as  its  breadth ;  if,  how- 
ever, the  spectrum  be  very  much  elongated,  the  white  will  totally 
disappear,  and  we  shall  distinguish  seven  principal  colors  in  it, 
in  the  following  order :  red,  orange,  yellow,  green,  blue,  indigo  and 
violet. 

These  colors  are  termed  prismatic,  and  simple  colors  of  the 
rainbow.  We  shall  soon  see  that  there  are  actually  a  very  great 
number  of  different  colors  in  the  spectrum,  but  that  among  these 
the  eye  distinguishes  the  seven  above  named. 


286  DIFFERENT  COLORED  RAYS. 

The  red  end  of  the  spectrum  is  always  turned  towards  the 
side  at  which  the  round,  white  sun-image  g,  Fig.  279,  would 
appear,  if  the  prism  did  not  intervene ;  the  red  rays  suffer,  there- 
fore, the  least  amount  of  deviation. 

If  the  opening  in  the  shutter  be  about  -^th  of  an  inch  in  dia- 
meter, when  the  refracting  angle  of  the  prism  is  60°,  and  the 
spectrum  is  received  at  a  distance  of  6  yards,  we  shall  obtain  a 
perfect  separation  of  the  colors ;  that  is,  the  spectrum  will  every- 
where appear  vividly  colored,  without  showing  any  trace  of  white 
in  the  centre ;  the  separate  colors  appear,  however,  purer  when 
the  opening  is  smaller. 

In  order  to  see  the  prismatic  image,  it  is  not  necessary  to  pro- 
duce a  solar  spectrum  by  means  of  a  prism  on  a  white  wall,  it 
being  sufficient  to  look  through  a  prism  towards  a  bright,  narrow 
object.  If,  for  instance,  we  look  at  the  flame  of  a  candle  through 
a  prism  held  vertically,  it  will  appear  considerably  extended,  and 
colored  in  the  manner  we  have  mentioned.  If  we  cut  a  small 
opening  of  about  iVth  of  an  inch  in  diameter,  in  the  shutter,  we 
shall  see  the  clear  sky  through  this  opening;  that  is,  a  light  disc 
upon  a  dark  ground.  If,  then,  we  look  at  this  disc  through  the 
prism,  we  shall  perceive,  instead  of  the  white  circle,  a  very  much 
elongated  colored  image,  to  which  all  that  we  have  said  of  the 
spectrum  cast  upon  the  wall,  equally  applies. 

The  differently  Colored  Rays  are  unequally  refrangible. — This 
follows  from  white  light  admitting  of  being  decomposed  by  the 
prism  into  rays  of  different  colors;  the  red  rays,  after  passing 
through  the  prism,  form  an  angle  with  the  violet,  the  violet  rays 
deviating  more  from  their  original  direction  than  the  red.  The 
violet  rays  are  most  strongly  refrangible,  and  the  red  the  least  so. 
The  green  rays  are  more  refrangible  than  the  red,  and  less  so 
than  the  violet,  because  in  the  spectrum  they  lie  between  the  red 
and  violet. 

If  we  were  to  suppose  for  a  moment  that  white  light  contained 
only  red  and  violet  rays,  it  is  evident  that,  instead  of  the  spectrum, 
we  should  only  have  two  solar  images  separated  from  each  other, 
of  which  the  one  would  be  red,  the  other  violet.  We  can,  in 
fact,  make  such  separate  images  apparent:  many  bodies,  for 
instance,  have  the  property  of  not  admitting  all  colored  rays 
to  pass  equally  well  through  them  ;  they,  consequently,  absorb 
certain  rays.  To  these  belong  colored  glasses  and  colored 


DIFFERENT  COLORED  RAYS.  287 

fluids.  If,  for  example,  we  fill  the  intermediate  space  between 
two  parallel  glass  plates  with  a  solution  of  sulphate  of  indigo, 
and  look  with  a  prism  through  this  solution  towards  an  opening 
in  the  shutter,  we  shall  see  two  divided  images  of  the  opening, 
one  red  and  the  other  blue.  We  obtain  the  same  result  by 
using  a  piece  of  dark  blue  glass  in  the  place  of  the  indigo 
solution. 

The  whole  spectrum  consists  of  a  series  of  circularly  formed 
images  succeeding  one  another,  and  partly  overlapping  each  other. 
The  smaller  the  opening  is  through  which  the  white  rays  fall  upon 
the  prism,  the  smaller 
will  be  the  separate 
round  images,  while,  at 
the  same  time,  the  cen- 
tres of  the  separate  co- 
lored images  do  not  ap- 
proach nearer,  and,  con- 
sequently, the  different 
colors  less  overlap  one 
another ;  the  smaller  the  opening  is,  the  purer  will  also  the  sepa- 
rate colors  appear. 

Each  color  of  the  Spectrum  is  simple. — Every  color  is  simple  if 
it  does  not  admit  of  being  further  decomposed  into  other  colors. 
We  will  now  show  that  this  property  is  really  characteristic  of  the 
prismatic  colors. 

If  we  receive  a  spectrum  upon  a  wall,  and  make  a  hole  some- 
where about  the  spot  on 

T--   i     ^i         •   i   ±  f  n  Fig.  281. 

which  the  violet  rays  fall, 
we  shall  arrest  all  the  other 
colors,  while  only  one  co- 
lored ray  passes  through 
the  opening ;  this  ray  does 
not  admit  of  being  in  any 
way  further  decomposed; 
and,  if  it  be  again  suffered 
to  pass  through  a  prism,  the  color  remains  unchanged. 

Newton  applied  the  term  homogeneous  to  simple  light ;  a  name 
that  has  been  generally  adopted. 

White  light  may  be  recomposed  from  the  simple  colors  of  the 
spectrum. — If  we  receive  the  spectrum  on  a  lens  /,  the  variously 


288 


ON    WHITE    LIGHT. 


Fig.  282. 


colored  rays  will  be  united  by  it  in  a  point  f,  and  if  the  sun's 
image  be  received  upon  a  ground-glass,  or  a  paper  screen,  it 
will  again  appear  dazzlingly  white,  notwithstanding  the  different- 
ly colored  rays  that  fell  upon  the  lens.  If,  instead  of  holding 
the  screen  at  the  focal  point  jf,  we  remove  it  further  from  the 
lens,  we  again  obtain  an  inverted  spectrum  /  uf,  Fig.  282,  a  proof 

that  the  differently 
colored  rays  cross 
each  other  at  f,  and 
if  we  apply  a  mirror 
at  that  point,  the  re- 
flected rays  will  again 
form  a  spectrum  u" 
r". 

We  may  also  use  a 
concave  mirror  instead  of  a  lens  for  these  experiments. 

That  the  combination  of  prismatic  colors  yields  white,  is  proved 
by  the  extraordinary  experiments  made  by  Newton,  that  the  long 
prismatic  image,  seen  through  a  second  prism,  will,  under  favora- 
ble circumstances,  again  appear  as  a  perfectly  white  and  round 
disc.  Let  v  w  be  a  spectrum,  Fig.  283,  produced  by  the  prism, 
and  caught  on  a  white  wall.  If,  now,  a  second  prism  B  be  so 
placed  that  it  would  produce  the  same  spectrum  r  v  in  the  same 
place,  if  a  ray  of  solar  light  fell  upon  it  in  the  direction  o  n,  it  is 
clear  that  the  rays  falling  from  the  spectrum  on  the  prism  B  will 

emer£e  in  the  di' 
rection  n  o  ;  thus 

an  eye  at  o  must 
see  a  round  white 
image  of  the  co- 
lored spectrum  in 
the  direction  on  s. 
The  position  that 
must  be  given  to 
the  prism  B  may 
easily  be  ascer- 
tained by  experi- 
ment. 

If,  now,  we  divide  a  circular  disc  into  seven  sectors,  and  paint 
them  with  colors  that  most  nearly  approach  the  prismatic  hues, 


Fig.  283. 


COMPLEMENTARY   COLORS.  289 

the  disc,  if  made  to  rotate  rapidly,  will  no  longer  appear  to  be 
colored,  but  will  look  whitish,  and  it  would  appear  wholly  white, 
if  the  sections  could  be  painted  with  purely  prismatic  colors,  and 
if  the  breadth  of  the  separate  colored  sectors  stood  exactly  in  the 
same  relation  to  each  other  as  the  breadths  of  the  corresponding 
parts  of  the  spectrum.  Munchow  combined  the  prism  with  clock- 
work, in  order  to  be  able  to  make  experiments  with  pure  prismatic 
colors  on  this  principle,  by  setting  the  prism  into  rapid  oscillating 
motion.  By  this  motion  of  the  prism,  the  spectrum  moves  rapidly 
backward  and  forward  on  a  screen,  and  then  there  appears,  in- 
stead of  the  colored  spectrum,  a  white  band  of  light,  slightly 
colored  at  the  ends.  The  eye  rapidly  receives  at  each  of  the 
points  of  the  screen  the  impressions  of  all  the  separate  colors  suc- 
cessively ;  these  separate  impressions  vanish,  however,  and  pro- 
duce the  sensation  of  white. 

Of  the  Complementary  Colors,  and  the  Natural  Colors  of  bo- 
dies.— As  all  simple  colors,  combined  in  proper  proportions,  (that 
is,  in  the  proportion  given  by  the  spectrum,)  produce  white  light, 
it  is  sufficient  to  suppress  one  or  more  of  the  simple  colors,  or 
even  simply  to  alter  their  proportion,  to  form  any  shade  of  color 
from  white.  If,  for  instance,  we  suppress  the  red  of  the  spectrum 
in  white  light,  while  all  the  colors  remain  unaltered,  we  shall 
have  a  bluish  tint,  to  which  we  need  only  add  red,  in  order  to 
restore  the  white.  Two  tints  of  color  fulfilling  these  conditions, 
that  is,  giving,  when  combined,  white,  are  termed  complementary 
colors.  Each  color  has  its  complementary  color,  for  if  it  be  not 
white,  it  is  deficient  in  certain  rays  that  would  aid  in  producing 
the  white,  and  these  absent  rays  compose  the  complementary 
color.  Violet,  which  passes  more  or  less  into  red,  is  the  comple- 
mentary color  of  different  shades  of  green.  We  have  already 
seen  that  a  solution  of  sulphate  of  indigo  in  a  prism  yields  a  blue 
and  red  image  of  a  white  object.  The  red  image  is  very  sharply 
defined,  the  blue  not  so  much  so,  passing  somewhat  more  into 
violet,  and  less  into  green ;  the  light  transmitted  through  a  solu- 
tion of  indigo  is  therefore  wholly  deficient  in  yellow  and  orange, 
and  almost  so  with  respect  to  all  the  green,  and  a  portion  of  the 
violet.  These  absent  colors  form,  however,  when  taken  together, 
a  mixture,  in  which  yellow  predominates  to  a  considerable  extent ; 
yellow  is  consequently  the  complementary  color  to  blue  in  the 
indigo  solution ;  as  yellow  shades  of  color  are  complementary  to 
25 


290  NATURAL    COLORS    OF    BODIES. 

blue.     The  more  the  image  approaches  the  green,  the  more  will 
the  complementary  yellow  merge  into  red. 

We  shall  subsequently  have  another  opportunity  of  speaking  of 
complementary  colors. 

The  prism  we  have  made  use  of  to  decompose  solar  light,  will 
also  serve  to  analyze  the  natural  colors  of  bodies ;  and  for  this 
purpose,  we  need  only  cut  off  narrow  strips  from  colored  bodies, 
and  look  at  them  through  the  prism. 

We  glue  a  row  of  colored  strips  of  paper,  about  1  millimetre 
(0.039  in.)  wide,  and  as  seen  at  Fig.  284,  upon  a  piece  of  black 
Fi    284  paper:  let  1  be  white;  2,  yellow;  3,  orange; 

4,  scarlet;  5,  green;  and  6  blue;  the  best 
paper  for  the  purpose  is  that  used  by  book- 
binders for  the  titles  of  the  back  of  books, 
as  the  colors  are  generally  clear,  and  well 
defined.  If,  now,  we  look  at  these  colored 
strips  from  the  distance  of  several  feet,  through 
a  prism  whose  axis  is  parallel  with  the  direc- 
tion of  the  length  of  the  strips,  they  will  natu- 
rally appear  moved  out  of  their  places  ;  at  the 
same  time,  however,  all  the  colors  will  be  de- 
composed into  their  elementary  colors.  The 
white  paper  will  give  a  perfect  spectrum  with  all  colors,  from  the 
extreme  red  to  the  extreme  violet.  The  colored  image  given  by 
the  yellow  paper  approaches  most  nearly  to  the  perfect  spectrum. 
Red,  orange,  yellow  and  green  are  present;  the  lower  blue  and 
violet  end  alone  is  wanting ;  consequently  the  color  of  the  yellow 
paper  requires  only  blue  and  violet  in  order  to  produce  white.  The 
colored  image  of  the  piece  of  paper  No.  3  (orange)  is  much  less 
complete;  here  the  green  rays  are  wanting  as  well  as  the  violet 
and  blue.  The  colored  image  of  the  red  paper,  No.  4,  is  the  least 
dispersed,  showing  besides  red,  only  a  little  orange ;  the  red  of  this 
paper  is,  therefore,  almost  a  pure  prismatic  red.  In  the  colors  of 
the  paper  we  have  hitherto  considered,  red  was  contained  in  1  to 
4 ;  the  limits  of  these  four  colored  images  coincide,  therefore, 
above  in  a  straight  line,  while  below  they  are  cut  off  like  gradu- 
ated steps.  The  colors  of  the  papers  5  and  6,  green  and  blue, 
contain  but  very  little  red,  on  which  account  there  is  scarcely  any 
red  end  to  the  colored  images  they  yield ;  and  hence  it  follows 


DISPERSING   POWER   OF   DIFFERENT   SUBSTANCES.        291 

that  the  two  last  images  appear  much  more  removed  from  their 
true  position,  than  the  image  of  the  red  paper,  No.  4. 

If  we  look  through  the  prism  at  a  broad,  instead  of  a  narrow 
piece  of  paper,  we  shall  see  it  white  in  the  middle,  and  only 
colored  at  the  edges.  Supposing  that  we  look  at  the  white  strip 
of  paper  a  b,  in  Fig.  285,  through  a  prism  whose  axis  is 
at  right  angles  to  the  direction  of  length  of  the  paper,  the 
different  colored  images  of  the  band  will  appear  par- 
tially to  overlap  each  other.  The  red  image  of  the  band 
extends,  for  instance,  from  r  to  /,  the  orange  from 
o  to  </,  the  yellow  from  g  to  gf,  Sac. ;  the  violet,  finally, 
from  v  to  vr ;  it  is  thus  clear  that  the  images  of  all  the 
prismatic  colors  between  v  and  r1  coincide ;  the  whole 
spot  from  v  to  /,  must,  therefore,  appear  white.  There 
is  only  red  light  between  r  and  o ;  red  and  orange  be- 
tween o  and  gj  red,  orange,  and  yellow  between  g  and 
g  r\  the  red  end  of  the  image  will,  therefore,  pass  over 
to  a  yellowish  tint.  To  the  three  mentioned  colors, 
there  succeed  next  below  them,  green,  blue,  &c.  The 
upper  part  of  the  image  is  consequently  red,  passing 
gradually  through  yellow  to  white. 

The  other  end  of  the  image  is  violet,  and  passes  gradually 
through  blue  into  white. 

What  we  have  here  said  of  white  strips  of  paper,  applies  equally 
to  every  white  object  of  considerable  extension  seen  through  a 
prism,  appearing  colored  only  at  the  edges. 

A  broad  black  strip  upon  a  white  ground  affords,  when  seen 
through  a  prism,  exactly  the  contrary  phenomena ;  that  is  to  say, 
the  prismatic  image  at  the  end  which  is  least  refracted,  appears 
with  a  violet  and  blue  edge,  and  at  the  other  with  a  red  and  yel- 
low edge.  In  order  to  explain  this  inversion,  we  need  only  con- 
sider that  the  colors  are  produced  not  from  the  black  strip,  but 
from  the  white  surfaces  bounding  it.  If  the  black  strip  be  very 
narrow,  the  black  in  the  middle  will  entirely  disappear  from  the 
image. 

Of  the  Dispersing  Power  of  different  substances. — The  separa- 
tion of  the  different  rays  of  light  which  takes  place  in  their  pas- 
sage through  a  prism  is  designated  by  the  term  dispersion.  The 
dispersing  power  of  a  substance  is  great  in  proportion  to  the  dif- 


292        DISPERSING    POWER    OF    DIFFERENT    SUBSTANCES. 

ference  between  the  indices  of  refraction  of  the  red  and  violet 
rays. 

For  water  this  index  of  refraction  for  the  red  rays  is  1,330, 
while  that  for  the  violet  rays  is  1,344;  the  difference  of  the  two 
is,  therefore,  0,014.  For  flint-glass  the  indices  of  refraction  of 
the  red  and  violet  rays  are  1,628  and  1,671,  respectively;  the 
difference  is,  therefore,  0,043,  three  times  as  great  as  that  for 
water. 

If,  therefore,  we  make  a  water-prism,  which,  properly  placed, 
shall  refract  the  rays  as  strongly  as  a  flint-glass  prism,  the  breadth 
of  the  spectrum  of  the  latter  will  be  three  times  that  of  the  spec- 
trum of  the  water-prism ;  the  dispersing  power  of  flint-glass  is 
consequently  three  times  as  great  as  that  of  water. 

For  crown-glass,  the  difference  between  the  indices  of  refrac- 
tion for  the  red  and  violet  rays  is  only  half  as  great  as  that  for 
flint-glass;  the  dispersive  power  of  flint-glass  is,  therefore,  twice 
as  great  as  that  of  crown-glass,  although  the  indices  of  refraction 
for  the  two  kinds  of  glass  are  very  nearly  equal. 

We  call  prisms  achromatic  when  they  have  the  property  of 
refracting  rays  of  light,  without,  at  the  same  time,  decomposing 
them  into  colors,  and  achromatic  lenses  are  those  in  which  the 
foci  of  the  different  rays  coincide  exactly,  showing  the  objects  free 
from  all  colored  edges.  Achromatism  was  long  considered  im- 
possible :  that  is  to  say,  it  was  not  believed  that  light  could  be 
refracted  without  decomposition.  Newton  himself  was  of  this 
opinion,  because  he  thought  that  dispersion  was  always  pro- 
portional to  the  refracting  power  of  bodies.  The  possibility  of 
achromatism  was  for  a  long  period  the  subject  of  discussion  be- 
tween the  most  distinguished  men  of  science  of  their  day,  as 
Euler,  Clairaut,  and  tfJllembert.  Hell  certainly  made  achromatic 
telescopes  as  early  as  the  year  1733,  but  he  did  not  publish  his 
discovery.  Dollond  also  made  instruments  of  this  kind  in  1757, 
and  he  made  them  publicly  known.  Dollond's  discovery  was, 
without  doubt,  an  event  of  the  highest  importance  to  astronomy ; 
in  order,  however,  to  give  it  its  full  signification,  it  was  first  ne- 
cessary to  develop  the  mathematical  theory  of  achromatism ;  with- 
out which,  it  would  be  impossible  to  make  the  necessary  practical 
improvements.  Even  in  the  present  day,  when  such  progress  has 
been  made  in  optics  with  relation  to  the  construction  of  glasses, 


DISPERSING   POWER   OF   DIFFERENT   SUBSTANCES.       293 

and  notwithstanding  all  the  assistance  rendered  by  the  calculus, 
achromatism  must  be  classed  amongst  the  most  delicate  problems, 
both  in  a  theoretical  and  practical  point  of  view.  In  a  work  of 
this  kind,  we  must,  of  course,  restrict  ourselves  to  the  development 
of  the  principles  only,  on  which  the  construction  of  achromatic 
prisms  and  lenses  depend. 

If  we  so  arrange  two  prisms  A  and  B,  Fig.  286,  that  the  re- 
fracting edges  are  directed  towards  opposite  sides,  the  action  of 
one  will  more  or  less  fully  destroy  that  of  the  other.  The  disper- 
sion of  color  produced  by  A  will  be  counteracted  by  that  occa- 
sioned by  the  prism  B,  if,  under  similar  circumstances,  each  of 
the  prisms  alone  gives  an  equally  large  spec- 
trum ;  for,  in  this  case,  the  action  of  the  prism 
B,  in  relation  to  the  dispersion  of  color,  is  ex- 
actly equal  to  that  of  the  prism  ./?,  and  vice 
versa. 

If  the  dispersion  were  actually  proportional 
to  the  refracting  power,  as  Newton  supposed, 
two  prisms  of  different  substances  could  only 
give  equal  spectra,  provided  the  deviation  pro- 
duced by  the  one  were  equal  to  that  by  the 
other;  if,  therefore,  two  prisms  of  the  kind  represented  at  Fig. 
286,  were  placed  together,  the  decomposition  of  color  would  be 
stopped  by  this  combination,  and  with  it  the  deviation  likewise. 

Later  experiments  have,  however,  shown,  as  we  have  mentioned, 
that  Newton  was  wrong  in  the  opinion  he  had  formed  on  this  sub- 
ject ;  thus,  for  instance,  dispersion  is  much  more  considerable  in 
flint-glass  than  in  crown-glass,  whilst  the  average  indices  of  re- 
fraction of  both  kinds  of  glass  do  not  very  essentially  differ;  with 
an  equal  deviation,  the  spectrum  of  a  prism  of  flint-glass  is  almost 
twice  as  great  as  that  of  a  prism  of  crown-glass. 

If  the  refracting  angle  of  a  prism  be  not  too  great,  we  may 
assume,  without  any  marked  error,  that  the  breadth  of  a  colored 
image  is  proportional  to  the  refracting  angle ;  supposing,  now,  that 
we  have  a  prism  of  crown-glass  of  25°,  we  may  easily  calculate 
the  angle  of  a  prism  of  flint-glass  giving  the  same  dispersion  of 
color.  As  the  total  dispersion  of  the  flint-glass  is  twice  as  great 
as  that  of  the  crown-glass,  the  refracting  angle  of  the  flint-glass 
must  also  be  twice  as  small :  that  is,  about  12J°.  The  dispersion 

25* 


294        DISPERSING   POWER    OF    DIFFERENT    SUBSTANCES. 

of  color  of  a  flint-glass  prism  of  12^°,  is  as  great  as  that  of  a 
crown-glass  prism  of  25° ;  two  such  prisms,  therefore,  combined 
in  the  manner  indicated  at  Fig.  286,  will  not  produce  any  further 
dispersion  of  color. 

But,  as  the  indices  of  refraction  of  both  kinds  of  glass  are 
generally  very  nearly  equal,  the  deviations  of  the  prisms  A  and  B 
will  be  nearly  as  their  refracting  angles ;  the  deviation  produced 
by  Jl  is  nearly  twice  as  great  as  that  produced  by  B ;  the  prism 
B  can,  therefore,  only  remove  about  half  the  deviation  produced  by 
Jl ;  the  combination  of  the  prisms  A  and  B  will,  therefore,  still 
produce  a  deviation,  but  not  any  dispersion  of  color. 

Every  simple  lens,  whatever  be  the  substance  from  which  it  is 
formed,  will  have  a  different  focus  for  every  different  kind  of  ray, 
because  the  indices  of  refraction  of  the  rays  of  different  colors 
are  not  equal.  The  focus  of  the  red  rays  lies  further  from  the 
lens  than  the  focus  of  the  violet  rays.  The  foci  of  the  red  and 
violet  rays  are  not  equi-distant  in  all  lenses,  as  this  distance 
depends,  on  the  one  hand,  upon  the  curvature  of  the  lenses,  and, 
on  the  other,  upon  the  dispersive  power  of  the  substance.  In  pro- 
portion as  the  curvature  of  the  lens  from  the  middle  towards  the 
edge  is  inconsiderable,  the  foci  for  the  different  colors  will  also  be 
nearer  to  each  other. 

The  consequence  of  this  last  mentioned  circumstance  is,  that  the 
images  of  such  lenses  appear  more  or  less  impure,  and  more  or  less 
bordered  with  colored  edges.  We  may  be  easily  convinced  of 
this  by  looking  at  the  letters  of  a  book  through  a  lens  of  great 
curvature,  or  by  producing  the  image  of  distant  objects  by  such  a 
lens  on  a  ground-glass  table,  when  everything  will,  in  like  manner, 
be  surrounded  by  colored  edges.  As  the  distinctness  of  images  in 
microscopes,  as  well  as  in  telescopes,  was  thus  materially  affected, 
the  discovery  of  the  construction  of  achromatic  lenses  was  of  the 
greatest  importance  in  practical  optics. 

The  achromatism  of  lenses  depends  upon  the  same  principles 
as  the  achromatism  of  prisms  ;  achromatic  lenses  are  composed  of 
simple  lenses  made  of  different  kinds  of  glass.  A  crown-glass 
and  a  flint-glass  lens  are  commonly  combined  together  for  this 
purpose.  The  action  of  lenses  upon  rays  of  different  colors  is 
such,  that  a  concave  lens  causes  the  violet  rays  to  converge  more 
strongly,  while  a  concave  lens  makes  them  diverge  more  power- 


DISPERSING   POWER   OF   DIFFERENT   SUBSTANCES.       295 

fully  than  the  red  rays ;  we  may,  therefore,  understand  how  a 
combination  of  a  concave  and  a  Fi    287 

convex  lens,  as  seen  at  Fig.  287, 
is  able  wholly  to  destroy  the  dis- 
persion of  color ;  if  the  two  lenses 
be  of  different  kinds  of  glass,  the 
dispersion  of  color  maybe  stopped 
without,  on  that  account,  the  refraction  ceasing. 

If  a  convex  lens  of  crown-glass,  and  a  concave  lens  of  flint- 
glass  produce  an  equally  strong  dispersion  of  color,  the  two  com- 
bined will  produce  no  dispersion  at  all ;  but  as  flint-glass  acts 
with  a  more  strongly  dispersive  power,  a  concave  lens  of  flint- 
glass  capable  of  destroying  the  dispersion  in  a  convex  lens  of 
crown-glass,  will  not  be  able  entirely  to  remove  the  convergency 
of  the  rays  caused  by  the  convex  lens;  the  two  lenses  taken 
together  will,  therefore,  act  as  a  convex  lens,  whilst  the  dispersion 
of  color  is  destroyed,  thus  forming  an  achromatic  lens. 


296  OF    THE    EYE    AND    OPTICAL    INSTRUMENTS. 


CHAPTER    IV. 

OF  THE  EYE  AND  OPTICAL  INSTRUMENTS. 

THE  sensations  of  light  and  of  color  depend  upon  an  impression 
on  special  nerves,  whose  delicate  extremities  are  distributed  as  a 
nervous  membrane,  named  the  retina.  The  sensation  of  darkness 
depends  upon  a  perfect  state  of  rest  in  this  nervous  membrane, 
every  irritation  producing  the  sensation  of  light ;  this  irritation  is 
most  especially  produced  by  rays  of  light  passing  from  bodies  in 
the  external  world  through  the  eye  to  the  retina,  although  the 
sensations  of  light  and  color  may  be  produced  by  other  causes, 
and  without  the  co-operation  of  rays  of  light  coming  from  without, 
as,  for  instance,  by  the  pressure  of  the  blood  (scintillations  before 
the  closed  eyes).  An  external  pressure  upon  the  closed  eye,  and 
an  electrical  discharge  are  likewise  capable  of  producing  sensa- 
tions of  light. 

To  distinguish  external  objects  by  the  sight,  it  is  not  sufficient 
that  the  rays  of  light,  passing  from  a  body,  should  fall  upon  the 
retina;  but  a  special  apparatus  is  also  necessary  for  the  purpose 
of  distributing  the  light,  by  which  means  the  rays  passing  from  a 
luminous  point  may  only  strike  one  definite  spot  of  the  retina, 
and  that  the  rays  of  light  coming  from  other  points  may  be  kept 
from  this  spot;  in  this  manner  the  different  parts  of  the  retina  are 
differently  affected,  and  a  distinction  of  objects  is  consequently 
rendered  possible.  Where  there  is  a  deficiency  of  such  an  appa- 
ratus for  distributing  light,  as  is  the  case  with  many  of  the  lower 
classes  of  animals,  there  is  actually  no  sight,  properly  so  called, 
but  simply  the  power  of  distinguishing  light  from  darkness,  day 
from  night;  yet  even  here  a  special  nervous  apparatus  is  neces- 
sary. 

The  apparatus  intended  for  the  isolation  of  the  impressions  of 
light,  is  not  arranged  in  the  same  manner  in  all  classes  of  animals: 
here  we  distinguish  two  essentially  different  kinds  of  eyes;  1,  the 


Ta7>.  // 


COMPOSITE   EYES.  297 

mosaic  composite  eyes  of  insects  and  Crustacea,  and,  2,  the  eyes 
of  vertebrata  provided  with  convex  lenses. 

Composite  Eyes. — Muller  was  the  first  to  throw  any  light  by 
his  classical  investigations  upon  mosaic  composite  eyes.  There 
are  a  very  great  number  of  transparent  small  cones,  standing 
rectangularly  upon  the  convex  retina,  and  only  those  rays  falling 
in  the  direction  of  the  axis  of  the  cone  can  reach  its  base  on  the 
retina.  All  laterally  incident  light  is  absorbed,  because  the  lateral 
walls  of  the  cone  are  invested  with  a  darkly- colored  pigment.  In 
Fig.  288,fcbg  is  a  section  of  the  convex  retina,  with  the  trans- 
parent cylinders  upon  it.  It  is  evident 
that  the  rays  passing  from  the  luminous 
point  A  can  only  strike  the  retina  in 
c  6,  the  base  of  the  truncated  cone  \ 
a  b  c  d-,  the  bases  of  the  two  cones  con- 
tiguous to  a  b  c  d  are  no  longer  struck 
by  the  rays  passing  from  A ;  a  luminous 
point  B  sends  its  rays  to  another  spot 
of  the  retina,  and  so  on.  All  the  light 
coming  from  points,  lying  on  the  pro- 
longation of  the  cone,  will  naturally  act 
upon  the  basis  of  such  a  transparent 
cone,  and  the  impressions  of  light  from  all  points,  sending  light 
on  the  basis  of  the  same  cone,  will  also  blend  together;  from 
which  we  see  that  the  distinctness  of  an  image  on  the  retina  is 
greater  in  proportion  to  the  number  of  cones.  Muller*  charac- 
terizes the  sight  of  such  eyes  with  striking  accuracy,  when  he 
says:  "An  image  formed  by  several  thousand  separate  points, 
each  of  which  corresponds  to  a  distant  field  of  vision  in  the  ex- 
ternal world,  will  resemble  a  piece  of  mosaic  work,  and  a  better 
idea  cannot  be  conceived  of  the  image  of  external  objects,  which 
will  be  depicted  on  the  retina  of  beings  endowed  with  such 
organs  of  vision,  than  by  such  a  comparison." 

The  size  of  the  field  of  vision  of  such  eyes,  naturally  depends 
upon  the  angle  made  by  the  axes  of  the  external  cones,  that  is, 
upon  the  convexity  of  the  eyes.  The  transparent  membrane 
covering  the  eye  exteriorly,  the  cornea,  is  generally  divided  into 
facettes,  each  separate  facette  corresponding  to  the  above  men- 


Miiller's  Physiology,  translated  by  Baly,  vol.  ii.  p.  1091, 


298  SIMPLE   EYES   WITH   CONVEX   LENSES. 

tioned  transparent  cone.  The  number  of  the  facettes  of  such  an 
eye  is  generally  very  great,  a  single  eye  containing  often  from  12 
to  20,000  such  facettes. 

All  insects  have  not  such  mosaic  composite  eyes;  spiders,  for 
instance,  have  simple  eyes  with  lenses,  entirely  formed  like  the 
eyes  of  the  vertebrate  animals ;  there  are,  also,  many  insects 
which,  besides  the  mosaic  composite  eyes,  have  also  simple  eyes 
with  lenses,  but  the  construction,  as  well  as  the  position  of  these, 
would  lead  us  to  conjecture  that  they  are  only  intended  for  seeing 
the  most  contiguous  objects. 

Simple  Eyes  with  Convex  Lenses. — The  image  is  formed  upon 
the  retina  of  eyes  having  collective  lenses  in  precisely  the  same 
manner  as  the  images  of  ordinary  convex  lenses  ;  the  rays  issuing 
from  one  point  of  the  object,  and  striking  the  anterior  surface  of 
the  eye,  are  refracted  by  the  transparent  media  of  that  organ 
towards  a  point  of  the  retina.  Fig.  289  represents  the  section  of 

a  human  eye.  The  whole 
globe  of  the  eye  is  surrounded 
by  a  firm,  hard  membrane, 
only  transparent  at  the  front 
part ;  this  transparent  portion 
is  called  the  cornea,  and  the 
white  opaque  part,  the  tunica 
sclerotica;  the  transparent  cornea  is  more  strongly  curved  than 
the  rest  of  the  globe.  Behind  the  cornea  lies  the  colored  prismatic 
membrane,  the  iris,  which  is  plane,  cutting  off,  as  it  were,  the 
curvature  of  the  transparent  cornea  from  the  remaining  parts  of 
the  eye.  In  the  middle  of  the  iris,  at  s  sr,  there  is  a  circular 
opening,  which,  seen  from  the  front,  appears  perfectly  black;  this 
opening  bears  the  name  of  the  pupil.  Behind  the  iris  and  pupil 
is  the  crystaline  lens  c  </,  within  a  transparent  capsule,  by  which 
it  is  also  attached  to  the  outer  wall  of  the  eye.  Between  the  lens 
and  the  cornea,  there  is  a  clear  and  somewhat  saline  fluid  (humor 
aqueus),  while  the  whole  space  behind  the  lens  is  filled  with  a 
transparent  gelatinous  substance  (humor  vitreus).  The  crystal- 
ine lens  itself  is  flatter  anteriorly  than  posteriorly. 

Within  the  sclerotica,  in  the  interior  of  the  eye,  is  the  choroid 
membrane  (tunica  choroidea),  and  within  this  lies  the  retina,  which 
is  an  expansion  of  the  optic  nerve.  The  choroid  membrane, 
which  invests  the  whole  inner  cavity  of  the  eye,  is  covered  over 


DISTINCT   VISION   AT   DIFFERENT   DISTANCES.  299 

with  a  black  pigment,  the  object  of  which  is  to  prevent  the  purity 
of  the  image  being  disturbed  by  reflection  within  the  eye.  For 
the  same  reason,  the  interior  surface  of  telescopes  is  stained 
black. 

The  rays  of  light  that  fall  upon  the  eye  strike  the  front  of 
the  sclerotica,  (the  white  of  the  eye,)  and  are  irregularly  distri- 
buted in  all  directions,  or  they  enter  the  eye  through  the  cornea ; 
the  external  rays  of  the  pencil,  passing  through  the  cornea,  fall 
upon  the  iris,  and  are  irregularly  distributed  in  all  directions,  by 
which  means  the  color  of  the  iris  becomes  visible.  The  central 
rays  pass  through  the  pupil  to  the  lens,  and  are  thence  refracted 
towards  the  retina  in  such  a  manner,  that  the  rays,  passing  from 
a  point  of  an  external  object  through  the  pupil,  are  again  united 
in  a  point  upon  the  retina.  Thus,  an  image  of  the  object  before 
the  eye  is  impressed  upon  the  retina.  In  Fig.  289,  m  is  the  image 
of  the  point  /,  and  m!  the  image  of  I'. 

We  may  prove,  by  an  experiment  on  the  eye  of  an  ox,  or  a 
horse,  that  a  diminished  inverted  image  of  the  object  before  the 
eye  is  really  impressed  upon  the  retina.  We  must  carefully  open 
the  eye  in  order  to  be  enabled  to  see  the  retina  through  the  vitre- 
ous humor ;  then  if  the  eye  be  directed  towards  a  window,  or  any 
bright  object,  we  distinctly  see  a  diminished  inverted  image  of  it 
upon  the  retina.  This  is  most  clearly  seen  in  animals  in  which 
the  choroid  is  destitute  of  pigment,  as  in  white  rabbits,  whilst,  at 
the  same  time,  the  back  part  of  the  sclerotica  is  transparent.  In 
such  eyes,  the  images  on  the  retina  may  be  seen  without  further 
preparation. 

Distinct  Vision  at  Different  Distances. — We  have  already  seen 
that  the  image  of  a  lens  changes  its  position  if  the  object  be  ad- 
vanced nearer,  or  removed  further  away  ;  the  image  recedes  further 
from  the  glass  in  proportion  as  the  object  approaches  it.  As  the 
eye  acts  entirely  like  a  lens,  and  we  are  only  able  to  see  objects 
clearly  when  the  points  of  union  of  the  refracted  rays  fall  exactly 
upon  the  retina,  we  might  suppose  that  we  could  only  see  objects 
at  a  definite  distance,  when  the  image  was  sharply  defined  upon 
the  retina ;  experience  shows,  however,  that  the  contrary  is  the 
case,  and  that  a  sound  eye  can  distinctly  see  all  objects  when  re- 
moved more  than  eight  inches  from  it :  it  must,  therefore,  have 
the  capacity  of  accommodating  itself  to  different  distances. 

We  may  show  this  by  a  very  simple  experiment :  if  we  make 


300  DISTINCT    VISION    AT    DIFFERENT    DISTANCES. 

a  small  black  spot  upon  a  transparent  glass  plate,  and  hold  it 
from  10  to  12  inches  from  the  eye,  we  may  see  at  pleasure  either 
the  spot,  or  the  distant  objects  through  the  glass  plane.  If  we 
see  the  remote  objects  distinctly,  the  spot  will  appear  cloudy  and 
undefined,  while,  on  the  other  hand,  distant  objects  will  be  dis- 
torted when  the  spot  is  seen  with  distinctness ;  when,  therefore, 
distant  objects  appear  distinct,  the  rays  passing  from  the  dark 
spot  are  not  limited  upon  the  retina,  and  conversely :  the  eye  has 
thus  the  capacity  of  adapting  itself  to  seeing  at  small  and  great 
distances. 

If,  now,  the  rays  passing  from  a  luminous  point  are  united  be- 
fore or  behind  the  retina,  a  small  circle  of  dispersion  will  be 
formed  upon  the  retina  instead  of  the  bright  point,  and  this  is 
the  reason  that  objects  at  a  distance,  to  which  the  eye  cannot  ac- 
commodate itself,  appear  indistinct.  This  power  of  adaptation  has 
its  limits,  for  if  the  object  be  brought  too  near  the  eye,  that  organ 
is  no  longer  able  to  make  those  alternations  necessary  for  causing 
the  image  to  fall  upon  the  retina,  in  which  case  the  points  of 
union  lie  behind  that  membrane,  and  circles  of  dispersion  of  the 
separate  luminous  points,  instead  of  the  sharply  defined  image, 
are  formed  upon  it ; .  so  that  it  is  no  longer  possible  to  distinguish 
the  figures.  A  pin's  head,  for  instance,  cannot  be  distinctly  seen 
when  held  at  1  or  2  inches  only  from  the  eye. 

As  the  point  of  union  of  rays  from  the  lens  is  the  more  distant 
as  the  objects  approach  nearer  to  it,  we  may  explain  distinct  vision, 
at  different  distances,  by  the  assumption  that  the  length  of  the 
axis  of  the  eye  may  be  increased  or  diminished  at  pleasure ;  the 
axis  of  the  eye  must  be  longer  for  near,  than  for  distant  objects, 
or,  in  other  words,  the  retina  is  further  removed  from  the  cornea 
for  near  objects.  Olbers  has  calculated  the  prolongation  of  the 
axis  of  the  eye  necessary  to  explain  distinct  vision  at  a  distance 
extending  from  4  inches  to  infinity.  The  numbers  given  in  the 
following  little  table  are  taken  from  these  calculations. 


DISTANCE  OF  THE  OBJECT. 

DISTANCE  OF  THE  IMAGE  FROM 
THE  CORNEA. 

Infinite. 
27  inches. 
8       " 
4       « 

0,8997  inches. 
0,9189      « 
0,9671      « 
1,0426      « 

DISTANCE   OF   DISTINCT   VISION.  301 

According  to  this  calculation,  a  prolongation  of  the  axis  of  the 
eye  of  about  1  inch  would  suffice,  without  any  change  of  curva- 
ture of  the  lens  and  the  cornea,  to  explain  distinct  vision  from  4 
inches  to  infinity. 

If  we  would  explain  the  power  of  adaptation  of  the  eye  by  a 
change  of  the  curvature  of  the  cornea,  we  must,  according  to 
Olbers*  calculations,  assume  the  following  variations : 


DISTANCE  OF  THE  OBJECT. 

RADIUS  OF  THE  CORJfEA. 

Infinite. 
27  inches. 
20       " 
5       " 

0,333  inches. 
0,321      " 
0,303      " 
0,273      « 

If  thus  the  radius  of  curvature  of  the  cornea  were  only  altered 
from  0,333  to  0,300,  and  the  axis  of  the  eye  could  be  lengthened 
or  shortened  about  half  a  line,  the  power  of  adaptation  possessed 
by  the  eye  for  all  distances  from  4  inches  to  infinity,  would  admit 
of  explanation. 

However  such  an  assumption  may  explain  the  power  of  adapta- 
tion possessed  by  the  eye,  its  correctness  is  by  no  means  proved ; 
in  fact,  many  objections  have  been  raised  against  it,  and  at  any 
rate  so  great  a  change  in  the  curvature  of  the  cornea  is  somewhat 
improbable. 

Other  physiologists  endeavor  to  explain  this  power  of  adapta- 
tion of  the  eye  by  the  compression  and  change  of  position  of  the 
lens,  and  although  this  may  be  probable,  it  is  by  no  means  proved 
with  certainty.  This  capacity  may,  perhaps,  be  derived  from  a 
co-operation  of  all  these  causes. 

Distance  of  Distinct  Vision.  Short-sightedness  and  long-sighted- 
ness.— It  has  already  been  observed,  that  objects,  when  brought 
too  near  the  eye,  can  no  longer  be  distinctly  seen.  There  is  a 
certain  distance  for  every  eye,  beyond  which  an  object  must  not 
be  placed  if  it  is  to  be  distinctly  seen  without  exertion ;  at  this 
distance  of  distinct  vision  we  involuntarily  hold  a  book  in  read- 
ing, if  it  be  printed  with  type  of  ordinary  size.  If  we  bring  the 
object  nearer,  it  cannot  be  seen  without  effort,  while,  at  a  still 
closer  proximity,  distinct  vision  is  no  longer  possible.  In  a  per- 
fectly sound  eye,  the  distance  of  distinct  vision  is  about  8  or  10 
26 


302  DISTANCE    OF    DISTINCT    VISION. 

inches:  where  this  distance  is  less,  we  term  the  eye  short-sighted; 
where  it  is  greater,  long-sighted. 

Indistinctness  of  vision,  with  reference  to  objects  in  close 
proximity,  arises,  as  we  have  already  observed,  from  the  rays 
passing  from  the  point  of  a  near  object,  diverging  so  strongly  that 
the  refracting  media  of  the  eye  are  no  longer  able  to  make  them 
sufficiently  convergent  to  produce  a  reunion  upon  the  retina ;  as 
the  point  of  union  falls  in  this  case  behind  the  retina,  they  appear 
with  a  circle  of  dispersion.  If  we  are  able  to  hinder  the  forma- 
tion of  this  circle  of  dispersion,  we  may  see  objects  when  brought 
very  near  to  the  eye. 

If  we  look  through  a  hole  made  with  a  pin  in  a  card,  holding 
the  eye  close  to  it,  we  shall  still  distinctly  see  the  letters  of  a 
book,  which  will  appear  considerably  enlarged,  whilst,  on  the 
removal  of  the  card,  we  shall  no  longer  be  able  to  distinguish  the 
letters.  The  reason  of  this  is,  that  rays  can  only  reach  the  eye 
from  one  point  of  the  neighboring  object,  passing  in  one  direction 
only,  through  the  fine  opening  in  the  card,  and  these  will  also 
strike  the  retina  in  one  point  only,  whilst,  if  the  card  do  not  keep 
off  the  other  rays,  a  whole  pencil  will  pass  from  one  point  of  the 
object  through  the  pupil  into  the  eye,  forming  a  circle  of  dis- 
persion upon  the  retina. 

We  may  here  mention  the  interesting  and  instructive  experi- 
ment of  Father  Scheiner.*  If  we  make,  in  a  card,  two  minute 
orifices,  with  a  needle,  at  a  smaller  distance  from  each  other  than 
the  diameter  of  the  pupil,  and  hold  these  openings  close  to  the 
eye,  we  see  a  double  image  of  a  small  object,  as  a  pin's  head, 
held  within  the  visual  distance.  From  this  small  object  there 
pass  two  very  minute  pencils  of  rays  through  the  apertures  into 
the  eye.  These  rays  converge  towards  a  point  lying  behind  the 
retina,  falling  upon  the  latter  at  two  different  points ;  these  are 
two  isolated  points  of  the  circle  of  dispersion,  which  would  arise 
upon  the  retina,  if  the  other  rays  were  not  intercepted  by  the 
card. 

If,  now,  we  remove  the  small  object  more  and  more,  the  images 
will  approach,  because  the  rays  falling  upon  the  eye  through  the 
apertures  will  diverge  less,  and  consequently  be  refracted  towards 
a  point  lying  nearer  to  the  retina.  If  the  object  be  removed  from 
the  eye  to  the  distance  of  distinct  vision,  the  two  images  will  per- 

*  Ocules  sine  Fundamentum  Opticum,  etc.,  1652. 


SHORT-SIGHTEDNESS,   MYOPIA,   PRESBYOPIA.  303 

fectly  coincide,  since  all  rays,  passing  from  one  point  lying  exactly 
at  the  distance  of  distinct  vision,  will  be  concentrated  at  one  point 
of  the  retina. 

We  naturally  see  near  and  distant  objects  with  equal  distinct- 
ness through  a  fine  aperture  in  a  card,  held  close  before  the  eye, 
without  there  being  any  necessity  for  the  eye  to  accommodate 
itself  to  the  distances,  since  the  rays,  passing  from  one  point  of 
the  object,  only  strike  the  retina  at  one  point;  through  such  an 
aperture,  we  may,  therefore,  at  the  same  time,  distinctly  see  near 
and  distant  objects;  we  may  here  ask  what  are  the  conditions  of 
adaptation  necessary  for  an  eye  in  looking  through  a  fine  aper- 
ture? And  the  answer  naturally  is,  that  in  its  normal  condition, 
for  the  maintenance  of  which  no  effort  is  necessary,  the  eye  is  in 
the  state  requisite  for  seeing  objects  which  lie  at  the  distance  of 
distinct  vision. 

Let  us  now  revert  to  Schemer's  experiment:  if  a  distant  object 
be  observed  through  both  openings,  the  rays  passing  into  the  eye, 
through  these  two  apertures,  must  evidently  meet  at  one  point 
before  the  retina,  as  the  condition  of  each  adaptation  does  not 
change  in  the  eye ;  but  the  two  pencils  diverge  again  behind  the 
point  of  intersection,  striking  the  retina  at  two  different  points, 
when  consequently  distant  objects  will  be  seen  double.  Through 
the  two  small  apertures,  therefore)  we  only  see  a  small  object  single, 
when  it  lies  at  the  distance  of  distinct  vision. 

On  the  principles  deduced  from  Schemer's  experiments,  instru- 
ments have  been  constructed  which  bear  the  name  of  optometers, 
and  serve  to  define  the  distance  of  distinct  vision. 

Short-sightedness,  Myopia,  and  long-sightedness,  Presbyopia, 
are  defects,  the  causes  of  which  must  be  sought  for  in  a  deficiency 
of  the  power  of  adaptation,  on  which  habit  exercises  a  very  inju- 
rious effect;  short-sightedness  often  arises  from  the  neglect  of 
exercising  the  sight  on  distant  objects,  and  children  who  bend  the 
head  too  closely  over  the  paper  in  writing  or  reading,  frequently 
become  short-sighted  in  consequence.  A  prolonged  use  of  the 
microscope  will  cause  an  otherwise  sound  eye  to  become  tempo- 
rarily short-sighted,  this  condition  frequently  continuing  for  some 
hours.* 

The  simplest  method  of  improving  either  defect  consists,  as  we 
have  already  stated,  in  holding  a  card  having  a  fine  aperture  close 

*  Muller's  Physiology. 


304  ACHROMATISM    OF    THE    EYE. 

to  the  eye.  By  this  means,  the  principle  of  which  has  already 
been  explained,  the  distinctness  of  the  image  will  certainly  be 
restored  at  the  expense  of  the  clearness. 

Another  method  is  the  use  of  spectacles,  which  are  constructed 
with  concave  glasses  for  short-sighted  eyes,  and  with  convex 
glasses  for  long-sighted  eyes.  In  a  short-sighted  eye,  the  images 
of  distant  objects  fall  before  the  retina,  and  the  eye  has  not  the 
power  of  accommodating  itself  in  such  a  manner  that  the  images 
can  be  formed  upon  the  retina;  we,  therefore,  on  this  account 
alter  the  refractive  power  of  the  eye,  by  the  use  of  concave  glasses, 
by  means  of  which  the  rays  coming  to  the  eye  converge  less 
strongly,  and  thus  enable  the  rays  to  unite  upon  the  retina. 

In  far-sighted  persons  the  image  of  contiguous  objects  falls 
behind  the  retina,  without  the  eye  being  able  to  accommodate 
itself  to  this  condition  of  refraction;  we  therefore  use  convex 
glasses  to  make  the  rays  more  convergent,  and  thus  bring  the 
point  of  union  upon  the  retina. 

More  or  less  strong  glasses  must  be  employed  where  there  is 
more  or  less  short-sightedness  present;  and  the  object  to  be  at- 
tended to  in  the  choice  of  the  glasses,  is  that,  in  co-operation  with 
them,  the  distance  of  distinct  vision  may  be  rendered  the  same 
as  in  a  perfectly  sound  eye,  that  is  about  8  or  10  inches. 

Short-sightedness  appears  more  frequently  in  middle  age,  and 
long-sightedness  in  old  age. 

Achromatism  of  the  Eye. — In  ordinary  lenses,  the  foci  of  the 
rays  of  different  color  do  not  coincide,  and  hence  arise  those 
colored  edges  which  we  perceive  on  the  outlines  of  objects  seen 
through  a  common  lens ;  that  is,  if  the  opening  of  the  lens  is 
large,  and  the  objects  are  not  in  the  middle  of  the  field  of  view. 
We  have  already  seen  how  lenses  may  be  made  achromatic,  or 
free  from  this  defect.  The  human  eye  is  likewise  an  achromatic 
instrument,  for  we  see  the  objects  pure  and  without  colored  bor- 
ders. 

As  the  achromatism  of  lenses  may  be  effected  by  a  combination 
of  different  refracting  substances,  and  of  unequal  dispersive  power, 
the  possibility  of  the  achromatism  of  the  eye  may  easily  be  con- 
ceived, since  a  ray  of  light,  in  its  course  through  that  organ,  has 
to  traverse  successively  three  different  media,  which,  when  taken 
together,  act  as  an  achromatic  lens. 

The  eye  is  not,  however,  perfectly  achromatic,  for  we  only  see 


RELATION  BETWEEN  PERCEPTION  OF  THE  EYE,  ETC.  305 

an  object  pure,  if  the  eye  can  properly  accommodate  itself  to  the 
distance  of  this  object.  We  see,  for  instance,  very  vividly  colored 
edges  on  a  dark  object  lying  before  the  eye,  if  we  look  beyond  it 
upon  distant  objects,  and  see  these  distinctly;  if,  for  instance, we 
make  a  hole  of  about  1  line  in  diameter,  and  holding  it  5  or  6 
inches  from  the  eye,  look  through  it  towards  some  distant  object, 
the  edges  of  the  opening  will  appear  colored. 

Relation  between  the  Perception  of  the  Eye  and  the  External 
World. — The  act  of  vision  depends  essentially  upon  the  impres- 
sions on  the  retina  being  reduced  to  a  state  of  consciousness  by 
certain  means  unaccountable  to  us.  We  actually  only  take  cogni- 
zance of  one  definite  condition,  one  certain  affection  of  the  retina; 
but  that  we  convert  the  images  of  the  retina  at  once  into  repre- 
sentations of  the  external  world,  is  an  act  of  immediate  and  spon- 
taneous judgment,  and  we  have  attained  such  certainty  in  this, 
by  constant  self-corroborating  experience,  that  we  do  not  feel  the 
retina  to  be  a  perceptive  organ,  and  confuse  the  direct  impressions 
with  what,  according  to  our  judgment,  is  the  cause  of  them.  This 
substitution  of  the  judgment  for  sensation  occurs  involuntarily, 
and  so  to  say,  has  become  a  second  nature  to  us. 

As  we  put  for  the  impression  upon  the  retina  a  representation 
of  the  external  world,  we,  in  like  manner,  substitute  an  object 
external  to  us  for  every  image  on  the  retina.  That  we  seek  in  a 
definite  direction  the  object  corresponding  to  a  definite  image  of 
the  retina,  is  as  much  the  result  of  continuous  consequent  expe- 
rience as  the  action  of  our  sense  of  sight  with  reference  to  the 
external  world. 

If  we  suppose  the  object  and  its  image  on  the  retina  connected 
by  a  straight  line,  this  is  the  direction  in  which  we  perceive  the 
images  externally.  Volkmann  has  shown  that  if  we  draw  a  straight 
line  from  each  point  of  the  image  on  the  retina  towards  the  cor- 
responding points  in  the  external  world,  all  lines  will  intersect 
each  other  at  one  point,  lying  in  the  interior  of  the  eye  and  be- 
hind the  lens ;  this  point  he  calls  the  point  of  intersection. 

It  has  been  already  shown  that  diminished  and  inverted  images 
are  formed  upon  the  retina,  and  hence  the  question  arises,  why  we 
do  not  see  all  things  inverted*}  This  question  is  satisfactorily 
answered  in  the  above  considerations.  The  knowledge  of  the 
existence  of  an  image  on  the  retina,  and  of  its  lying  on  the  upper 
and  lower  parts  of  the  retina,  on  its  right  or  left  side,  can  only  be 

26* 


306      RELATION    BETWEEN    PERCEPTION    OF    THE    EYE,  ETC. 

attained  by  optical  investigations;  the  sensation  of  the  retina  does 
not  occur  as  consciousness,  but  is  involuntarily  projected  exter- 
nally in  a  certain  direction,  namely,  that  in  which  the  objects  lie 
that  cause  the  images  on  the  retina.  In  this  direction,  however, 
we  also  find  objects  by  other  perceptions  of  sense ;  as,  for  example, 
by  the  sense  of  feeling ;  there  is  consequently  the  greatest  har- 
mony between  the  different  perceptions  of  sense  in  relation  to 
locality;  and  without  such  a  state  of  harmonious  accord,  we 
should  see  objects  inverted. 

With  the  representation  of  external  things,  by  means  of  the 
organ  of  vision,  we  combine  also  a  representation  of  their  size 
and  distance.  The  images  on  the  retina  lie  side  by  side,  and  if 
we  do  not  recognize  the  corresponding  objects  to  be  immediately 
contiguous  to  each  other,  but  situated  the  one  behind  the  other, 
that  is,  if  we  raise  ourselves  from  the  plane  on  which  our  obser- 
vations are  made,  to  an  imaginary  representation  of  the  depth  of 
space,  this  is  an  act  of  the  understanding,  and  not  of  sensation. 
The  young  child  has  no  conception  of  distance,  and  grasps  at  the 
moon,  as  at  an  object  immediately  within  his  reach.  The  con- 
ception of  the  depth  of  visual  space  is  only  acquired  by  moving  in 
space,  by  observing  that  images  change  by  this  motion,  and  ena- 
bling us  by  our  own  change  of  place  to  form  an  idea  of  the  dis- 
tance of  objects. 

The  apparent  size  of  objects  depends  upon  the  size  of  the  image 
on  the  retina.  If  we  suppose  lines  drawn  from  both  extremities 
of  the  image  on  the  retina,  towards  the  corresponding  extreme 
points  of  the  object,  these  lines  will  intersect  each  other  at  an 
angle  x,  which  we  call  the  angle  of  vision ;  the  size  of  this  angle 
is,  however,  proportional  to  the  size  of  the  image  on  the  retina, 
and  we  may  therefore  say  that  the  apparent  size  of  objects  depends 
upon  the  size  of  the  visual  angle  under  which  they  appear.  Two 
objects  of  different  size,  as  Ji  B  and  A'  B',  may  have  the  same 

apparent  size,  if  their  size  be 

Fig   290  . 

proportional  to  their  distance 
from  the  eye;  different  objects, 
therefore,  whose  sizes  are  as 
1:2:  3,  &c.,  will  appear  at 
once,  twice,  thrice  the  dis- 
tance under  an  equally  great 
angle  of  vision. 


VISION   WITH   BOTH   EYES. 


307 


Our  judgment,  regarding  the  actual  size  of  objects,  and  their 
distance,  is  only  acquired  by  continued  experience,  and  may  by 
practice  attain  a  most  extraordinary  degree  of  certainty. 

Vision  with  both  Eyes. — When  we  direct  both  eyes  to  one  ob- 
ject, we  see  only  a  single  image,  provided  the  eye  accommodate 
itself  to  the  distance  at  which  the  object  is  placed;  we  always 
see  a  double  image  if  the  eye  accommodates  itself  to  a  greater 
or  smaller  distance ;  we  see  it  sharply  and  distinctly  when  we 
see  it  singly ;  and  it  appears  indistinct  and  distorted  when  seen 
doubly. 

We  may,  at  will,  see  a  single  or  double  image,  by  holding 
before  the  face  one  or  two  fingers  exactly  behind  the  other,  at  a 
distance  of  about  1  and  2  feet,  when  the  back  one  will  appear 
double,  if  we  direct  the  axes  of  the  eyes  to  the  foremost  one,  and 
vice-versa. 

In  Fig.  291,  L  and  R  are  the  two  eyes,  A  and  B  two  objects 


Fig.  291. 


Fig.  292. 


lying  at  different  distances.  If  we  look  at  the  object  A,  the  axes 
of  both  eyes  (the  axis  of  the  eye  is  the  straight  line  connecting 
the  middle  of  the  retina  with  the  central  point  of  the  lens,  and 
the  pupil)  will  be  directed  towards*^,  and  will  consequently  make 
a  tolerably  large  angle  with  each  other ;  the  image  of  Jl  appears 
in  each  eye  upon  the  middle  of  the  retina  ;  if,  now,  we  look  at  the 
distant  object  B,  as  represented  in  Fig.  292,  the  angle  of  the 


308  VISION    WITH    BOTH    EYES. 

axes  of  the  eyes  will  be  smaller,  and  the  image  of  B  will  appear 
in  each  eye  in  the  middle  of  the  retina. 

If  we  look  at  A,  as  represented  in  Fig.  291,  the  image  of  B 
will  lie  to  the  right  of  the  middle  of  the  retina  in  the  left  eye,  and 
to  the  left  of  it  in  the  right  eye ;  the  images  b  and  b'  do  not, 
therefore,  lie  in  corresponding  parts  in  both  eyes,  and  this  is  pro- 
bably the  reason  of  the  object  B  being  seen  double.  As  the 
image  b  lies  to  the  right  of  a  in  the  left  eye,  B  will  appear  to  be 
to  the  left  of  A,  whilst  the  right  eye  sees  the  object  B  to  the  right 
of  A,  the  image  b'  being  left  of  a'.  If  we  have  fixed  both  eyes 
on  the  object ./?,  in  such  a  manner  that  we  only  see  it  single, 
whilst  B  appears  double,  we  may  make  the  left  or  right  image 
of  B  disappear,  according  as  we  receive  the  rays  passing  from 
B  upon  the  left  or  right  eye.  If,  on  the  contrary,  we  see  the 
distant  object  B  in  such  a  manner  that  A  appears  double,  as  in 
Fig.  292,  the  image  of  A  on  the  right  will  disappear,  if  we  cover 
the  left  eye. 

It  is  not  necessary  that  both  axes  of  the  eye  should  be  exactly 
fixed  upon  an  object  to  enable  us  to  see  a  single  image  with  both 
eyes,  that  is,  the  image  need  not  fall  in  the  middle  of  the  retina 
in  each  eye,  since,  in  that  case,  we  could  only  see  one  object  single, 
while  all  others  would  appear  double.  A  whole  series  of  objects 
may,  at  the  same  time,  be  seen  single  with  both  eyes,  if  they 
only  cast  their  image  on  corresponding  parts  of  the  retina  in  both 
eyes.  In  Fig.  293,  L  and  R  represent  the  two  eyes,  A  B  and 

C  three  different  objects  lying  be- 
fore them  ;  the  images  of  the  three 
objects  follow  the  same  order  in  both 
eyes,  that  is  to  say,  the  image  of  B 
lies  in  the  middle,  the  image  of  Cto 
the  left,  and  that  of  A  to  the  right, 
upon  the  retina  of  both  eyes ;  as  the 
images  c  and  c'  on  the  retina,  lie  to 
the  left  of  b  and  6,  both  eyes  see  the 
object  Cto  the  right  of  B-,  in  the 
same  manner,  both  eyes  see  the  ob- 
ject A  to  the  left  of  B,  as  the  images 
a  and  a'  on  the  retina  are  to  the  right  of  b  and  V. 

If  an  object  appears  single  to  both  eyes,  that  is,  if  its  image 
falls  upon  corresponding  parts  of  the  retina  in  both  eyes,  we  see 


LIMITS    OF   VISIBILITY.  309 

it  more  clearly  than  with  one  eye,  and  of  this  we  may  easily  con- 
vince ourselves  by  looking  at  a  strip  of  white  paper,  and  then  hold- 
ing up  a  black  screen  in  such  a  manner  as  to  conceal  half  the 
paper  from  one  eye,  the  portion  of  paper  seen  simultaneously  by 
both  eyes,  appears  higher  than  the  other  half,  which  is  only  seen 
by  one  eye. 

The  reason  of  our  being  able  to  see  singly  with  both  eyes,  is 
probably  to  be  sought  in  the  course  of  the  various  fibres,  and  not 
as  the  consequence  of  habit.  Miiller,  in  whose  writings  much 
may  be  found  regarding  the  different  experiments  that  have  been 
made  to  elucidate  this  wonderful  chain  of  causes,  says,  "  The 
eyes  may  be  compared  to  two  branches  with  a  single  root,  of 
which  every  minute  portion  bifurcates  so  as  to  send  a  twig  to  each 
eye." 

Limits  of  Visibility. — In  order  that  an  object  continue  visible, 
it  is  necessary  that  the  angle  of  vision,  under  which  it  appears, 
should  be  within  certain  limits,  depending  very  much  upon  the 
light  transmitted  by  the  object,  and  its  color,  the  nature  of  the 
back-ground,  and  the  individual  characteristics  of  the  eye.  To 
an  eye  of  ordinary  power,  an  object  is  still  visible  with  a  moderate 
degree  of  light,  at  an  angle  of  30  seconds,  and  a  light  object,  as 
a  silver  wire,  maybe  seen  on  a  dark  back-ground  under  an  angle 
of  vision  of  2  seconds.  Dark  bodies  may  also  be  very  distinctly 
seen  on  a  white  ground,  even  when  they  are  very  minute  ;  thus 
an  eye  of  moderate  power  may  see  a  hair,  when  held  against  a 
tolerably  clear  sky,  at  a  distance  of  4  or  6  feet. 

Duration  of  the  Impression  of  Light. — If  we  describe  a  circle 
rapidly  with  a  burning  coal,  we  are  unable  to  distinguish  the  coal 
itself,  seeing  only  a  fiery  circle.  The  cause  of  this  phenomenon 
arises  from  the  part  of  the  retina,  affected  by  an  impression  of 
light,  not  recovering  its  tranquillity  instantaneously  after  the  im- 
pression itself  has  ceased ;  from  the  same  rea-  Fig  294< 
son  we  are  unable  to  distinguish  the  spokes  of 
a  rapidly  revolving  wheel,  and  the  upper  sur- 
face of  a  top  painted  with  alternate  sectors  of 
black  and  white,  as  seen  in  Fig.  294,  will  appear 
gray.  But  if  the  top,  after  rotation  in  the  dark, 
be  lighted  by  a  flash  of  lightning,  or  an  electric 
spark,  we  are  able  clearly  to  distinguish  the  separate  sectors. 

If  we  make  two  holes,  diametrically  opposite  to  each  other,  in 


310 


DURATION    OF    THE    IMPRESSION    OF    LIGHT. 


a  paste-board  disc,  of  2  or  3  inches  in  diameter,  and  draw  strings 
through  them,  as  seen  in  Figs.  295  and  296,  we  may,  by  means 
of  the  threads,  cause  the  disc  to  revolve  so  rapidly  as  to  show 
alternately  first  the  one  side  and  then  the  other.  If  we  then  make, 
on  one  side,  a  black  stripe  in  the  direction  of  the  two  little  holes, 
and,  on  the  other  side,  one  at  right  angles  with  them,  we  shall  see 

Fig.  295.  Fig.  296. 


Fig.  297. 


a  cross  on  making  the  figure  revolve  rapidly,  because  the  impres- 
sion produced  upon  the  eye  by  the  horizontal  stripe  is  not  oblite- 
rated when  the  vertical  stripe  becomes  visible.  If  we  paint  a  cage 
on  one  side,  and  a  bird  on  the  other,  the  bird  will  appear  to  be 
within  the  cage  on  making  the  figure  revolve  rapidly. 

A  very  ingenious  and  pretty  apparatus  has  been  constructed, 

on  the  principle  of  the 
duration  of  the  impres- 
sion of  light,  and  is 
called  the  phenakisti- 
scope,  or  the  magic  disc. 
A  disc  of  8  or  9  inch- 
es in  diameter,  may 
be  put  into  a  rapid 
rotatory  motion  about  a 
horizontal  axis  x\  at 
the  edge  of  which  there 
is  a  succession  of  aper- 
tures at  equal  distances 
from  each  other.  In  the 
magic  disc  represented 
in  Fig.  297,  there  are 
8  such  apertures.  To 
the  circle  formed  with- 
in these  8  apertures,  a 
smaller  and  painted 
disc  is  fastened,  on 
which  the  same  object 


DURATION   OF   THE   IMPRESSION   OF   LIGHT.  311 

is  represented  in  8  different  positions,  each  aperture  correspond- 
ing to  a  different  position.  In  our  figure  a  very  simple  object, 
merely  a  pendulum,  has  been  delineated.  Under  the  opening  1, 
the  pendulum  is  represented  as  having  attained  its  extreme  posi- 
tion to  the  left ;  under  2,  we  see  it  nearer  to  its  position  of  equi- 
librium ;  at  3,  it  has  reached  this  point,  &c.  This  apparatus  must 
now  be  held  before  a  looking-glass,  in  such  a  manner  that  its 
painted  side  may  be  turned  towards  the  glass,  on  which  we  are  to 
see  the  reflection  of  the  colored  disc  through  one  of  the  openings,  the 
upper  one  for  instance.  As  the  disc  revolves,  one  opening  after 
the  other  passes  before  the  eye,  but  as  the  intervening  spaces 
pass  before  us,  nothing  will  be  seen.  If  we  assume  that  at  a  defi- 
nite moment,  the  opening  1  passes  before  the  eye,  we  shall  see 
below  it  the  pendulum  in  its  greatest  deviation ;  the  impression  of 
light  received  by  the  eye  at  this  moment  will  remain  until  the 
second  opening  has  come  before  the  eye,  and  now  the  pendulum 
will  appear  in  the  same  place  as  when  seen  in  its  greatest  stage 
of  deviation,  but  somewhat  nearer  to  a  position  of  equilibrium; 
the  image  of  this  second  position  will  remain  in  the  eye  until  that 
of  the  third  position  has  come  to  the  same  point,  and  then  we 
shall  see  the  pendulum  in  a  state  of  equilibrium ;  the  representa- 
tions of  the  pendulum,  passing  thus  successively  before  the  eye, 
cause  the  deceptive  impression  that  we  actually  see  the  pendulum 
oscillate.  Instead  of  a  pendulum,  we  may  choose  some  other 
object,  and  represent  it  in  as  many  different  positions  as  there  are 
apertures,  so  that  each  one  of  the  latter  may  correspond  to  a  dif- 
ferent position  of  the  object.  The  movements  of  men  or  animals 
may,  in  this  manner,  be  most  successfully  given  by  merely  repre- 
senting them  in  different  and  successive  phases. 

As  objects  must  have  a  certain  magnitude,  in  order  to  be  per- 
ceptible to  the  eye,  so  must  also  the  impression  of  light  endure 
for  an  appreciable  time,  in  order  to  produce  an  impression  upon 
the  retina.  For  this  reason  we  do  not  see  a  very  rapid  body,  as 
a  cannon-ball;  the  image  of  the  flying  ball  passing  over  the  retina 
with  such  rapidity  as  to  prevent  its  being  perceived  by  any  part  of  it. 

The  after  effects  produced  upon  the  retina  will  be  stronger, 
and  last  longer  the  more  intense  and  lasting  the  primitive  effect 
is.  The  after-images  of  light  objects  will  be  light,  and  those  of 
dark  objects  dark,  if  the  eye  be  withdrawn  from  all  subsequent 
action  of  light.  If,  for  instance,  we  look  for  a  length  of  time  con- 


312  COLORED  SECONDARY  IMAGES. 

tinuously  through  a  window  towards  the  clear  sky,  and  turning 
suddenly  away,  close  the  eye,  we  shall  still  see  the  light  interven- 
ing spaces  bounded  by  the  dark  window-frames ;  if,  on  the  con- 
trary, we  turn  the  eye  towards  a  white  wall,  the  after-image 
which  was  originally  dark  will  appear  light,  and  inversely;  thus 
we  shall  see  the  window-frames  light,  and  the  intervening  spaces 
dark.  This  inversion  is  easily  explained ;  if  the  eye,  already 
dazzled,  be  turned  towards  the  white  wall,  the  parts  of  the  retina 
previously  affected  by  the  bright  light  will  be  less  sensitive  to  the 
white  light  of  the  white  wall  than  those  parts  on  which  the  image 
of  the  dark  window  frames  has  fallen. 

Colored  Secondary  Images. — Our  organs  of  vision  often  expe- 
rience impressions  of  light  not  immediately  produced  by  external 
objects,  but  arising  from  a  peculiarly  irritable  condition  of  the 
retina.  Such  colors  are  termed  subjective,  and  also  physiological. 
To  these  belong  colored  secondary  images,  and  the  colors  pro- 
duced by  contrast. 

The  secondary  images,  of  which  we  have  spoken  in  a  previous 
part  of  this  chapter,  are  always  more  or  less  colored,  and  this 
coloration  is  deeper  in  proportion  to  the  intensity  of  the  primitive 
impression  of  light  occasioning  the  secondary  image.  If,  for  in- 
stance, we  look  for  some  time  fixedly  at  a  wax  taper,  and,  closing 
the  eye,  turn  towards  a  dark  part  of  the  room,  we  shall  still  seem 
to  have  the  flame  before  our  eyes,  although  it  changes  its  color  by 
degrees ;  at  first,  it  becomes  quite  yellow,  passing  then  from  orange 
to  red,  next  from  red,  through  violet,  into  a  greenish  blue,  which 
becomes  darker  until  the  secondary  image  entirely  disappears. 
If,  on  the  contrary,  we  turn  the  eye,  that  has  been  dazzled  by  the 
flame,  towards  a  white  wall,  the  colors  of  the  secondary  image 
will  succeed  each  other  in  an  almost  inverse  order,  that  is,  we 
shall,  at  first,  see  a  dark  image  upon  a  light  ground,  becoming 
blue,  green,  and  yellow;  and,  finally,  blending  with  the  white 
ground,  so  as  to  be  no  longer  distinguishable  from  it,  when  the 
secondary  image  has  quite  disappeared,  that  is,  when  the  retina 
has  recovered  itself.  The  transition  from  one  color  to  another 
begins  at  the  margin,  and  distributes  itself  gradually  towards  the 
middle.  We  may  observe  similar  phenomena  in  the  dazzling 
images  of  white  paper  lying  upon  a  black  ground,  and  lighted  up 
by  the  sun,  &c. 

If,  while  the  colored  secondary  image  still  remains  in  the  closed 


COLORS    OF   CONTRAST.  313 

eye,  the  eye  is  opened,  and  directed  towards  a  white  wall,  we 
shall  see,  upon  the  latter,  an  image  complementary  to  the  one 
seen,  at  the  same  time,  on  closing  the  eye.  If  the  secondary 
image  were  red  to  the  closed  eye,  on  opening  the  eye,  and  direct- 
ing it  to  a  white  surface,  we  should  see  a  green  image. 

If  we  look  fixedly,  for  some  time,  at  a  colored  spot,  on  a  white 
ground,  we  shall  see  a  secondary  image  in  the  complementary 
colors ;  if  the  spot  were  blue,  the  secondary  image  would  be 
yellow;  if  it  were  red,  the  secondary  image  would  be  green,  &c. 
This  phenomenon  is  caused  by  the  retina  becoming  more  indif- 
ferent to  the  color  of  the  object,  and  consequently  more  sensitive 
for  those  colors,  contained  in  white  light,  which  are  not  in  the 
tints  of  the  object  producing  the  dazzling  effect. 

The  reason  of  the  retina  becoming  gradually  indifferent  to  a 
color,  by  looking  at  a  strongly  lighted  object,  of  the  same  hue,  is, 
that  the  color  grows,  by  degrees,  more  and  more  faint  and  unap- 
parent.  We  can  most  easily  convince  ourselves  of  this  in  the 
following  manner.  If,  after  looking  fixedly  for  a  long  time  at  a 
red  square  resting  upon  a  white  ground,  we  turn 
the  eye  somewhat  aside,  so  that  the  complement- 
ary secondary  image  may  still  fall  partially  upon 
the  colored  square,  as  represented  in  Fig.  298, 
we  shall  see  the  free  portion  of  the  secondary 
image,  green,  whilst  the  portion  of  the  original 
image  which  has  become  free,  (that  is,  the  part 
sending  its  rays  to  those  places  on  the  retina  which  had  not  pre- 
viously been  impressed  by  the  red  light,)  will  appear  to  be  of  a 
bright  red ;  where  the  two  squares  touch  each  other,  however,  we 
shall  see  a  far  fainter  red,  for  the  rays,  passing  from  this  portion 
of  the  objective  red  square,  impinge  upon  the  same  parts  of  the 
retina  which  have  already  become  less  sensitive  to  the  impression 
of  red  light. 

Colors  of  Contrast. — A  gray  spot  appears  darker  on  a  white 
surface,  and  lighter  on  a  black  one,  than  if  the  whole  surface 
were  covered  with  the  same  gray  tint.  The  following  experiment 
shows  this  very  clearly.  If  we  bring  a  narrow  opaque  body,  such 
as  a  pencil,  for  instance,  between  the  flame  of  a  taper  and  a  white 
surface,  we  shall  see  a  dark  shadow  upon  a  light  ground ;  if, 
then,  we  place  a  second  flame  near  the  first,  we  shall  see  two 
dark  shadows  upon  the  light  ground ;  but  yet  each  one  of  these 
27 


314  COLORS    OF    CONTRAST. 

shadows  is  as  strongly  illumined  by  the  flame  as  the  whole  sur- 
face was  before,  although  we  considered  the  surface  previously 
to  be  light,  while  the  shadow  appears  now  to  be  dark:  this  expe- 
riment shows  the  important  effect  produced  by  contrast. 

The  phenomena  of  contrast  are  still  more  striking  in  consider- 
ing colored  objects,  in  which  we  often  see  complementary  tints 
which  were  not  objectively  before  present. 

When  we  lay  a  narrow  strip  of  gray  paper  upon  light  green 
paper,  it  will  appear  reddish  ;  while,  if  we  lay  it  upon  blue  paper, 
it  will  appear  to  be  yellow ;  in  short,  it  will  always  be  comple- 
mentary to  the  color  of  the  ground.  This  experiment  is  very 
clearly  seen  if  we  glue  a  strip  of  white  paper  of  about  0-039 
inch  in  width  to  a  plate  of  colored  glass,  and  then  look  through 
it  towards  some  white  surface,  as  a  sheet  of  white  paper,  or  also, 
if  we  entirely  cover  one  side  of  the  glass  with  thin  paper,  and 
fastening  the  narrow  strip  to  the  other  side,  hold  the  glass  before 
the  flame  of  a  taper;  the  strip  will  then  appear  complementary 
to  the  color  of  the  glass,  consequently  red  upon  a  green  glass, 
and  blue  upon  a  yellow  glass,  &c. 

We  must  here  include  the  colored  shadows  which  appear  when 
a  narrow  body  throws  a  shadow,  or  colored  light,  and  when  this 
shadow  is  illuminated  by  white  light.  Such  shadows  as  these 
are  most  easily  obtained  in  the  following  manner :  If  we  let  rays 
of  light  fall  through  a  colored  glass  upon  a  white  surface,  for 
instance,  a  piece  of  white  paper,  so  that  it  may  appear  colored, 
and  if  we  receive  upon  any  spot,  by  means  of  a  narrow  body,  the 
colored  rays  lighting  the  paper,  we  shall  obtain  a  narrow  shadow, 
only  lighted  up  by  the  white  daylight  distributed  around ;  the 
shadow  will  appear  complementary  to  the  color  of  the  ground;  if 
a  red  glass  be  used,  the  shadow  will  be  green ;  if  a  yellow  one  be 
used,  the  shadow  will  appear  blue,  &c.  The  colors  of  these 
shadows  are  purely  subjective. 

We  often  observe  colored  shadows,  which  are  really  objectively 
variegated ;  they  arise  where  a  body  casts  two  shadows  by  double 
illumination,  and  where  the  sources  of  light  are  of  various  colors, 
as  in  that  case  each  shadow  is  illuminated  by  light  of  different 
colors.  Such  colored  shadows  arise  when  the  bluish  light  of 
the  sky  falls  at  twilight  into  a  room  where  a  candle  is  burning; 
thus,  if  we  hold  a  rod  in  such  a  manner  that  it  shall  cast  one 
shadow  in  the  candlelight,  and  another  in  the  daylight,  upon  a 


THE    CAMERA    OBSCURA.  315 

white  surface,  we  shall  obtain  one  blue  and  one  yellow  shadow ; 
the  one  being  illuminated  only  by  the  bluish  daylight,  and  the 
other  by  the  yellowish  flame  ;  in  this  case,  also,  contrast  may  ex- 
ercise a  great  influence  upon  the  intensity  of  the  phenomenon  of 
coloration,  and,  consequently,  a  partially  objective  and  a  partially 
subjective  origin  may  be  ascribed  to  the  appearance. 

The  phenomena  of  colored  nebulous  images  may  be  explained 
by  the  circumstance 'that  when  a  portion  of  the  retina  is  affected 
by  colored  light,  this  direct  effect  reacts  upon  the  neighboring 
parts  of  the  retina  in  such  a  manner,  that  they  are  converted  into 
some  of  the  colors  complementary  to  the  primitive  impression. 

This  combination  of  mutually  complementary  colors  produces 
an  agreeable  impression  upon  the  eye,  as  may  be  easily  understood, 
if  we  consider  that  when  any  portion  of  the  retina  is  affected  by 
any  one  color,  it  will  manifest  an  effort  to  call  forth  the  contrast- 
ing color  on  the  neighboring  parts.  Every  combination  of  colors, 
not  complementary  to  each  other,  is,  on  the  contrary,  inharmonious, 
producing  an  impression  which  will  be  more  disagreeable  the 
more  intense  the  colors  are ;  combinations  of  this  kind  are  said  to 
be  glaring  and  repulsive:  thus,  for  instance,  while  a  green  uniform 
faced  with  crimson  will  produce  an  agreeable  impression,  a  red 
uniform  faced  with  yellow  will  be  universally  condemned  as  defi- 
cient in  good  taste. 

The  Camera  Obscura. — This  apparatus,  invented  by  a  Neapo- 
litan, Porta,  in  the  middle  of  the  seventeenth  century,  consists 
essentially  of  a  convergent  lens  of  somewhat  considerable  focal 
length,  by  which  the  image  of  remote  objects,  as  of  a  landscape, 
is  depicted;  in  order  to  heighten  the  effect  as  much  as  possible, 
it  is  necessary  to  exclude  carefully  from  the  plane  on  wThich  the 
images  are  thrown  all  lateral  light ;  the  image  must,  therefore,  be 
received  in  a  dark  chamber. 

The  forms  most  commonly  given  to  the  Camera  Obscura,  are 
represented   in  Figs.    299    and 
300.  Fig.  299  is  a  box  having  a  Fig'  299' 

projection  a  b  c  d,  in  which  a 
convergent  lens  b  c  is  inserted  ; 
the  rays  entering  the  dark  box 
through  this  lens  are  reflected 
upwards  by  a  glass  plane  in- 
clined at  an  angle  45°  towards 


316  THE   MAGNIFYING    LENS. 

the  axis  of  the  lens,  and  so  arranged  that  the  image  of  a  distant 
object  at  i  k  can  be  received  upon  a  ground  glass  plate.  The 
cover  g  h  serves  to  exclude  as  much  as  possible  all  extraneous 
light  from  the  image.  If  the  ground  side  of  the  glass  be  turned 
upwards,  we  may  trace  upon  it  with  a  pencil,  the  outline  of  the 
image  arising  at  i  k,  and  thus  obtain  a  drawing  of  the  objects 
true  to  nature. 

Fig.  300  represents  a  somewhat  hollow  box,  at  the  bottom  of 

which  a  sheet  of  white  paper  is  laid ; 

through  the  upper  surface  of  the  box 

[there  passes  a  tube  containing  the  con- 
""" .-^m  vergent  lens,  over  which  there  is  a  plane 

mirror  inclined  at  an  angle  of  45°  to- 
wards the  vertical.  The  rays  coming 
from  the  object  are  reflected  downward 
from  the  mirror,  so  that  the  image  is 
formed  on  the  surface  of  the  paper. 
This  image  is  very  bright,  owing  to  all 
the  lateral  light  having  been  excluded 
by  the  walls  of  the  box,  by  which  mean 
we  are  easily  enabled  to  trace  the  out- 
lines of  this  image  with  a  pencil. 

The  beauty  of  the  images  depicted  in  a  Camera  Obscura,  has 
excited  the  desire,  if  possible,  of  permanently  fixing  them,  and 
although  most  persons  have  regarded  this  object  as  impracticable, 
there  are  still  some  who  have  made  the  attempt.  Since  light  pro- 
duces chemical  actions,  as,  for  instance,  blackens  chloride  of  sil- 
ver, there  appears  at  any  rate  to  be  a  possibility  of  procuring 
permanent  impressions  of  the  images  formed  in  the  Camera  Ob~ 
scura.  We  will  presently  proceed  to  discuss  the  discovery  of 
Daguerre,  which  was  essentially  that  of  perpetuating,  in  a  most 
wonderful  manner,  the  images  of  the  Camera  Obscura. 

The  most  advantageous  construction  of  the  Camera  Obscura  for 
the  Daguerreotype  pictures,  is  that  given  to  it  by  Voigtldnder,  of 
Vienna.  The  lens  used  by  him  is  a  combination  of  crown-flint 
glass  lenses,  in  which  the  images  are  much  more  sharply  defined 
than  in  the  common  achromatic  lens. 

The  Magnifying  Lens  or  Simple  Microscope. — We  have  already 
seen  that  the  apparent  magnitude  of  an  object  depends  upon  that 
of  the  angle  of  vision  under  which  it  is  seen ;  the  angle  of  vision 


THE   MAGNIFYING   LENS.  317 

increases  in  amount,  in  proportion  as  the  object  is  brought  nearer 
to  the  eye ;  but  we  only  bring  it  within  certain  limits,  that  is, 
within  the  distance  of  distinct  vision  from  the  unaided  eye,  when 
we  would  distinguish  the  outlines  and  the  separate  parts ;  and 
consequently  the  magnitude  of  the  angle  of  vision  is  circum- 
scribed. Every  instrument  admitting  of  a  further  enlargement  of 
the  angle  of  vision  for  small  contiguous  objects  than  the  naked 
eye  allows  of,  is  called  a  microscope.  According  to  this  expla- 
nation, the  opening  in  the  card  described  above,  is  a  microscope, 
that  is  a  simple  microscope,  although  by  this  term,  we  generally 
only  designate  convex  lenses  of  small  focal  length. 

In  order  to  understand  how  a  simple  convex  lens  can  serve  as 
a  microscope,  we  must  look  at  Fig.  301.     If  V  JFbe  a  convex 

Fig.  301. 


lens,  and  A  B  an  object  lying  within  the  focal  length  of  the  glass, 
then  all  the  rays,  passing  from  a  point  of  the  object  A  J5,  will 
diverge  after  their  passage  through  the  lens,  exactly  as  if  they 
came  from  the  corresponding  point  of  the  image  a  b  as  we  have 
already  shown  ;  an  eye  behind  the  lens  will  be  able  to  see  the 
object  distinctly  through  the  lens,  if  the  image  a  b  be  at  the  dis- 
tance of  distinct  vision;  in  this  case,  however,  the  object  being 
much  nearer  to  the  eye,  we  should  consequently  be  unable  to 
see  it  without  the  lens.  The  magnifying  power  of  the  lens  de- 
pends, therefore,  essentially  upon  the  means  it  gives  us  of  bringing 
the  object  very  near  to  the  eye,  and  thus  naturally  increasing  the 
angle  of  vision.  To  determine  the  magnifying  power  produced  by 
the  lens,  we  must  compare  the  magnitude  of  the  angle  of  vision, 

27* 


318  THE   MAGNIFYING   LENS. 

under  which  the  image  a  b  appears  to  the  eye,  when  lying  at  the 
distance  of  distinct  vision,  with  that  of  the  angle  of  vision  under 
which  the  object  itself  would  appear  if  it  were  just  so  far  removed 
from  the  eye. 

The  angle  under  which  a  b  appears,  can  only  be  ascertained  if 
the  distance  of  the  glass  from  the  point  of  intersection  in  the  eye 
be  known  ;  but  as  we  hold  the  eye  close  to  the  glass,  the  thickness 
of  which  is  inconsiderable,  we  may,  without  any  marked  error, 
assume  that  the  point  of  intersection  coincides  with  the  central 
point  o  of  the  lens;  and  under  this  supposition  the  magnifying 
power  is  easily  calculated. 

Seen  from  O,  the  object  A  B  and  the  image  a  b  appear  under 
an  equal  angle  of  vision  ;  we  therefore  find  how  much  it  is  mag- 
nified, if  we  compare  the  angle  of  vision  under  which  Jl  B  appears 
with  that  under  which  the  same  object  would  appear  if  removed 
from  0  to  the  distance  of  distinct  vision,  that  is,  to  the  position  of 
the  image  a  b.  As  the  apparent  size  of  an  object  is  inversely 
proportionate  to  its  distance  from  the  eye,  so  is  the  angle  of  vision 
Jl  0  B  to  the  angle  under  which  JL  B  would  appear  if  seen  from 
0,  if  this  object  were  removed  to  a  6,  or  inversely,  as  the  distance 
of  the  object  Jl  B,  and  of  the  image  a  b  from  O.  If  we  designate 
as  d,  the  distance  of  the  image  from  0,  and  the  distance  of  the 

object  Jl  B  from  the  eye  as  x,  the  magnifying  power  will  be  —  ,  d 

x 

being  the  distance  of  distinct  vision. 

If  we  were  to  assume  what  certainly  is  not  the  case,  that  the 
image  is  within  the  distance  of  distinct  vision,  and  the  object  in 

the   focus   of  the   lens,  the  magnifying  power  would  be  _?  if 

f  represent  the  focal  length  of  the  glass.     This  expression  — 

does  not  certainly  give  us  the  true  value,  but  it  enables  us  to 
approximate  to  a  correct  estimate  of  the  magnifying  power  of  the 
lens. 

If  the  image  a  b  were  at  the  distance  d,  the  object  would  be 
within  the  focal  distance  ;  x  is  therefore  in  every  case  smaller 
*;  the  true  value  of  the  magnifying  power  is,  therefore,  at  all 


events,  somewhat  greater  than  -. 

»/ 
If,  for  instance,  the  distance  of  distinct  vision  be  10  inches, 


THE   SOLAR   MICROSCOPE.  319 

and  the  focal  length  of  the  lens  2  inches,  the  magnifying  power 
will  still  be  somewhat  more  than  — ,  that  is,  rather  more  than  5. 

The  smaller  the  value  of  f^  the  less  will  be  the  focal  distance 
of  the  lens ;  the  less  also  will  be  the  value  of  x  in  proportion  to 

the  greatness  of  the  value  of  — ,  and,  consequently,  the  greater 

will  be  the  magnifying  power.     A  lens  of  small  focal  distance 
magnifies  more  strongly  than  one  of  greater  focal  distance. 

The  Solar  Microscope. — This  instrument,  the  action  of  which 
is  the  most  interesting  and  instructive  in  optics,  consists  of  a 

Fig.  302. 


system  of  glasses  serving  to  illuminate  objects,  and  of  a  system 
of  lenses  of  short  focal  distances  giving  a  convergent  image  of  the 
objects. 

The  mirror  m,  Fig.  302,  reflects  the  solar  light  along  the  tube  t, 
parallel  with  its  axis.  The  lens  i  r  makes  the  rays  somewhat  con- 
vergent; a  second  lensy  increases  this  convergence  still  more,  so 
that  the  rays  are  united  at  a  focus,  which  is  very  near  to  the 
object  under  examination.  In  order  that  this  may  always  be  ren- 
dered possible,  the  lens  must  be  made  movable ;  this  motion  is 
imparted  by  a  screw,  the  head  of  which  is  outside  the  tube,  and 
let  into  a  little  notched  rod  fastened  to  the  setting  of  the  lens. 

The  objects  secured  between  or  upon  glass  plates,  are  brought 
between  the  metal  plates  p'  and  q.  As  the  plate  q  is  pressed  by 
springs  againt  pf,  the  objects  are  held  by  this  pressure,  and  thus 
prevented  from  slipping. 

If  the  object  be  properly  adjusted  and  illumined,  it  is  easy  to 
obtain  an  enlarged  image  of  it.  For  this  purpose  we  make  use 
of  the  achromatic  lens  /,  which  is  really  the  object-lens.  A 
notched  rod  is  fastened  to  the  setting  of  this  lens,  in  which  a  slide 
is  inserted,  by  which  the  lens  I  may  be  moved  at  will.  We  now 


320 


THE    COMPOUND    MICROSCOPE. 


adjust  the  lens  at  the  proper  distance  from  the  object,  until  we 
have  obtained  a  sharp,  clear  image  upon  a  white  wall,  a  piece  of 
linen,  or  a  paper  screen,  at  a  distance  of  10,  15  or  20  feet.  As 
an  actual  image  is  formed  here,  it  necessarily  follows  that  the 
object  must  be  at  the  other  side  of  the  focus  of  the  lens  /.  We 
may  calculate  the  magnifying  power,  by  dividing  the  distance  of 
the  object  from  the  lens  by  the  distance  of  the  image  from  it.  If, 
however,  we  want  to  observe  directly  the  amount  of  the  magnify- 
ing power,  we  must  make  use  of  a  glass  micrometer,  the  magni- 
tude of  whose  divisions  is  known,  and  then  measure  the  size  of 
the  divisions  in  the  image. 

Similar  microscopes  have  also  been  constructed  in  which  the 
light  of  the  sun  is  replaced  by  artificial  light,  as,  for  instance,  by 
the  light  of  a  ball  of  lime  (Drummond's  light),  ignited  by  the  oxy- 
hydrogen  blow-pipe,  or  by  the  light  of  a  lamp  of  great  illuminat- 
ing power.  The  magnifying  power  will  be  small  in  proportion 
to  the  smallness  of  the  illuminating  power  of  the  lamp. 

The  Magic  Lantern  depends  upon  similar  principles,  the  only 
difference  being,  that  the  objects  are  painted  in  large  dimensions 
upon  glass,  and  are  lighted  by  a  lamp  allowing,  at  most,  of  15  to 
20-fold  magnifying  power. 

The  Compound  Microscope. — The  principles  on  which  the  con- 
struction of  all  microscopes  depends,  however  different  in  their 
arrangements,  are  the  following: 

1.  The  objects  to  be  subjected 
to  observation,  are  placed  near  a 
convex  lens  6,  of  short  focal  dis- 
tance, and   somewhat  beyond  the 
focus.     This  lens  is  called  the  ob- 
ject  glass,  whether  it  be  simple  or 
compound,  achromatic  or  not  achro- 
matic. 

2.  The    actual    and    magnified 
images,    thrown    by    the    objects 
through  the  object-glass,  are  seen 
through    a  convex   lens   c,  which 
serves  here  as  a  microscope;  this 
second  lens  is  called  the  ocular  or 
eye-glass  of  the  microscope,  whether 
it  be  simple  or  compound,  achro- 
matic or  not  achromatic. 


Fi?.  303. 


THE   REFLECTING   TELESCOPE.  321 

Thus  every  dioptric  microscope  is  essentially  composed  of  an 
object-glass,  and  an  eye-glass;  and  the  magnifying  power  of  the 
microscope  is  the  product  of  the  magnifying  powers  produced  by 
these  glasses.  If,  for  instance,  the  object-glass  magnified  5  times, 
and  the  eye-glass  10  times,  such  a  microscope  would  consequently 
magnify  the  diameter  of  objects  50  times,  and  their  surfaces 
2500.  We  should  obtain  a  linear  power  of  1000,  and  a  super- 
ficial power  of  1,000,000  if  the  magnifying  powers  of  the  object- 
glass,  and  the  eye-glass  were  respectively  100  and  10,  or  50  and 
20,  or  40  and  25,  &c. 

The  Reflecting  Telescope. — We  apply  the  term  Telescope  to  all 
instruments  serving  to  show  distant  objects  magnified.  It  con- 
sists of  a  concave  mirror  or  a  converging  lens,  by  which  an 
image  of  distant  objects  is  produced,  which  is  seen  through  a 
simple  or  compound  eye-glass,  or  eye-piece.  If  the  image  be 
reflected  by  a  concave  mirror,  we  term  the  instrument  a  reflect- 
ing telescope.  Its  most  important  part  is  a  concave  mirror  of 
metal  turned  towards  the  object,  of  which  an  inverted  image  is 
produced  in  accordance  with  the  laws  we  have  already  treated 
of.  Different  telescopes  vary  only  in  the  manner  in  which  this 
image  is  observed. 

The  most  common  arrangement  adopted  in  the  construction  of 
these  telescopes  is  represented  in  Fig.  304.     The  concave  mirror 
m  mf  has  a  circular  aper- 
ture c  c'  in  its  centre ;  the 
incident  rays  are  so  re- 
flected that  a  real  inverted 
image  of  distant  objects  is 
formed  at  i  i' ;  this  image 
is   now  within  the   focal 

distance  of  the  small  concave  mirror  v,  by  which  an  upright 
image  of  the  inverted  image  i  i'  is  formed  before  the  eye-glass. 
The  eye-glass  is  composed  here,  as  in  the  microscope,  of  two 
lenses.  The  first  causes  the  rays  passing  from  the  mirror  v  to  be 
more  convergent,  and  consequently  moves  the  image  n  n'  some- 
what nearer  to  the  mirror  v,  than  would  be  the  case  if  it  were  not 
for  this  lens ;  the  image  n  n'  is  now  seen  through  the  lens  imme- 
diately before  the  eye. 

The  mirror  v  must  be  removed  from,  or  drawn  nearer  to,  the 


322 


REFRACTING    TELESCOPES. 


eye-glass,  in  proportion  to  the  greater  or  smaller  distance  of  the 
objects  to  be  observed;  this  is  effected  by  the  screw  b  s. 

Refracting  Telescopes. — In  some  telescopes,  a  converging  lens 
is  used  in  the  place  of  the  concave  mirror.  An  achromatic  lens 
should  be  chosen,  in  order  that  the  image  of  distant  objects, 
thrown  upon  the  object-glass,  may  be  clear  and  sharply  defined; 
such  an  object-glass  must,  therefore,  always  be  composed  of  two 
unequally  dispersive  substances;  two  lenses  being  generally  used 
that  are  in  immediate  contact,  as  we  have  already  described ; 
but  in  dialithic  telescopes,  the  achromatizing  flint-glass  lens  is 
removed  further  from  the  front  crown-glass  lens,  and  brought 
nearer  to  the  ocular,  so  that  the  former  may  have  a  smaller  dia- 
meter. Telescopes  differ  in  the  various  arrangements  of  the 
ocular.  In  Galileo's  telescope,  the  ocular  consists  of  a  simple 
biconcave  lens;  the  ocular  of  the  night,  or  astronomical  telescope, 
has  one  or  two  converging  lenses ;  while  the  terrestrial  telescope 
has  four. 

The  arrangement  of  Galileo's  telescope  is  represented  in  Fig. 
305.  V  Wis  the  object-glass,  which  would  produce  a  diminished 

Fig.  305. 


inverted  image  at  a  6,  if  the  rays  were  not  already  received  by  the 
concave  glass  X  Z.  But  now  the  eye-glass  is  so  placed  that  the 
distance  of  the  image  a  b  is  somewhat  greater  than  the  dispersive 
distance  of  the  concave  lens;  consequently,  all  rays  converging 
towards  one  point  of  the  image  a  b,  are  so  refracted  by  the  con- 
cave lens  that,  after  their  passage  through  it,  they  diverge  as  much 
as  if  they  came  from  a  point  before  the  glass  ;  the  rays  converging 
towards  b  diverge,  therefore,  as  if  they  came  from  B ;  and  those 
converging  towards  a,  as  if  they  came  from  JJ ;  we  thus  see  the 
erect  magnified  image  A  B  through  the  telescope. 

It  is  easy  to  calculate  the  magnifying  power  of  this  kind  of 
telescope,  if  we  know  the  focal  distance  of  the  object-glass,  and 
the  amount  of  dispersion  of  the  eye-glass.  The^angle  under  which 


REFRACTING    TELESCOPES.  323 

the  object  would  appear  without  the  telescope,  is  equal  to  the  angle 
under  which  the  image  a  b  appears  wrhen  seen  from  the  focus  of  the 
object-glass,  and  is,  consequently,  equal  to  the  angle  bp  a;  if  we 
suppose  the  eye  removed  to  the  focus  o  of  the  eye-glass,  the  object 
seen  through  the  telescope  will  appear  under  the  angle  Ji  o  B, 
which  is  equal  to  the  angle  boa,  in  order,  therefore,  to  deter- 
mine how  many  times  a  telescope  magnifies,  we  have  only  to  deter- 
mine how  many  times  the  angle  b  o  a  is  greater  than  the  angle 
b  p  a. 

The  distance  of  the  image  a  b  from  the  object-glass  is  equal  to 
the  focal  distance  f  of  the  latter,  if  the  object  be  very  far  removed ; 
but  the  distance  of  the  image  a  b  from  the  ocular,  is  not  percepti- 
bly larger  than  the  dispersive  distance  f  of  this  glass,  and  we 
may,  therefore,  without  any  serious  error,  consider  the  distance  of 
the  image  a  b  from  o  as  equal  to/7;  but  now  the  angles  bp  a  and 
b  o  a  are  inversely  very  nearly  as  this  distance,  therefore : 

bpa  :boa=f  if,  or  6_?_?  =  / 
bpa      f 

If  we  consider  the  angle  b  p  a,  under  which  the  object  appears 
without  a  telescope,  as  =  1,  we  shall  have  b  o  a,  the  angle  under 

/ 
which  it  will  be  seen  in  the  telescope  =yr;  that  is,  we  shall  find 

the  magnifying  power  by  dividing  the  focal  distance  of  the  object- 
glass  by  the  dispersive  (or  focal)  distance  of  the  eye-glass :  the 
magnifying  power  increases,  therefore,  directly  with  the  augmen- 
tation of  the  focal  distance  of  the  object-glass,  and  inversely  with 
the  dispersive  (or  focal)  distance  of  the  eye-glass. 

The  distance  of  the  two  glasses  is  evidently  very  nearly  equal 
toy — f\  if,  therefore,  we  join  different  eye-glasses  to  the  same 
object-glass,  the  distance  of  the  two  glasses  must  be  greater  in 
proportion  to  the  shortness  of  the  focal  length  of  the  eye-glass,  and 
therefore  to  the  increase  of  the  magnifying  power. 

In  astronomical  telescopes,  the  image  of  the  object-glass  is 
actually  formed,  and  is  seen  through  a  simple  or  compound  lens, 
as  represented  in  Fig.  306 ;  a  b  is  an  inverted  image,  formed  by 
the  object-glass  V  W,  of  an  object  which  is  examined  by  the 
lens  X  Z,  and  appears  magnified  at  A  B. 

The  magnifying  power  of  such  a  telescope  can  easily  be  cal- 
culated, if  we  know  the  focal  length  of  the  object-glass  and  the 
eye-glass,  for  the  angle  of  vision  under  which  the  object  appears 


324  REFRACTING    TELESCOPES. 

Fig.  306. 


to  the  naked  eye  is  equal  to  the  angle  under  which  the  image  a  b 
is  seen  from  the  middle  of  the  object-glass  V  W;  but  it  appears 
through  the  telescope  under  the  same  angle  as  the  image  b  a  seen 
from  the  middle  of  the  eye-glass  XZ;  but  one  of  these  angles  is 
to  the  other  inversely  as  the  distance  of  the  image  a  b  from  the 
object-glass  to  the  distance  from  the  eye-glass;  and  the  image  is 
at  the  focal  distance  f  from  the  object-glass,  and  the  distance  f 
from  the  eye-glass,  if  we  designate  the  focal  distance  of  the  eye- 
glass by^/*';  the  angle  of  vision  under  which  the  distant  object 
appears  when  seen  through  the  telescope,  is  to  the  angle  of  vision 
under  which  it  is  seen  by  the  naked  eye  as  fiof;  the  magnify- 
ing power  of  the  telescope  is,  therefore,  i« 

The  length  of  the  telescope  isf-\~ff;  that  is,  it  is  equal  to  the 
sum  of  the  focal  distances  of  both  glasses. 

In  general,  a  combination  of  two  lenses  is  made  use  of  instead 
of  one  simple  lens  for  the  eye-glass.  The  compound  eye-pieces  of 
astronomical  telescopes  are  arranged  either  precisely  like  the  com- 
pound eye-pieces  of  the  microscope — in  which  case  the  image  is 
formed  between  the  two  glasses  of  the  eye-piece — or  the  two 
lenses  are  placed  near  to  each  other,  so  that  the  image  is  formed 
before  the  eye-piece,  and  is  seen  through  both  lenses  as  through 
one  single  strong  one. 

It  is  evident  that  we  see  the  objects  inverted  through  an  astro- 
nomical telescope,  for  an  inverted  image  of  the  distant  object  is 
formed  upon  the  object-glass,  and  from  being  seen  through  a 
simple  magnifying  glass,  does  not  again  appear  erect. 

The  clearness  of  the  image  depends  upon  the  aperture  of  the 
object-glass,  and  the .  extent  of  the  field  of  view  upon  the  eye- 
glass. 

In  order  to  be  able  to  bring  the  objects  to  be  observed  within 
the  field  of  view  of  astronomical  telescopes,  a  cross  wire  must  be 


REFRACTING   TELESCOPES.  325 

applied,  exactly  at  the  spot  where  the  image  of  the  object  appears 
through  the  object-glass. 

Although  it  is  inexpedient  in  looking  at  terrestrial  objects  to  see 
everything  inverted,  it  matters  but  little  in  astronomical  observa- 
tions, or  in  making  measurements.  In  order  to  see  objects  erect, 
when  they  are  very  strongly  magnified,  the  eye-glass  of  the  astro- 
nomical telescope  is  replaced  by  a  tube  containing  four  convex 
lenses,  and  we  thus  obtain  the  terrestrial  telescope.  The  four 
lenses  in  the  eye-piece,  form,  in  some  degree,  a  magnifying  com- 
pound microscope  of  inconsiderable  power,  by  which  the  inverted 
image  is  made  to  appear  erect.  The  two  anterior  glasses  in  the 
eye-piece,  form,  in  some  respects,  the  object-glass  of  this  micro- 
scope, while  the  two  others  constitute  the  eye-glass. 

The  magnifying  powers  of  the  Galilean  and  the  astronomical 
telescopes  may  be  calculated,  as  we  have  already  seen,  by  the 
focal  distances  of  the  glasses ;  but,  as  this  focal  distance  has  first 
to  be  ascertained,  it  is  better  to  determine  the  amount  of  magnify- 
ing power  by  immediate  experiment.  This  may  be  simply  done 
in  the  following  manner:  we  place  at  some  distance  from  the 
telescope,  a  graduated  staff,  such  as  is  used  in  measuring  land, 
and,  while  we  keep  one  eye  directed  to  this,  we  look  through  the 
telescope  at  the  same  time  with  the  other ;  we  thus  observe  how 
many  divisions  of  the  graduated  staff  seen  by  the  naked  eye  fall 
upon  one  of  the  degrees  magnified  by  the  telescope,  and,  conse- 
quently, obtain  the  value  of  the  magnifying  power.  The  rows  of 
tiles  of  a  roof  will  answer  a  similar  purpose  to  that  of  the  graduated 
staff. 

Formerly,  dioptric  telescopes  were  very  imperfect,  as  achromatic 
object-glasses  had  not  then  been  applied  in  practice;  and  on  that 
account  a  concave  mirror  was  made  use  of  instead  of  the  object- 
lens,  and  thus  arose  the  reflecting  telescope. 


28 


326  PHENOMENA    OF    INTERFERENCE. 


CHAPTER   V. 

PHENOMENA    OF    INTERFERENCE. 

Two  different  hypotheses  have  been  advanced  to  explain  the 
different  phenomena  of  light,  namely,  the  theory  of  Emission,  or 
Corpuscular  theory,  and  the  theory  of  Vibration,  or  Undulatory 
theory. 

The  theory  of  emission  assumes  that  there  is  a  peculiar  substance 
of  light,  and  that  a  luminous  body  transmits  particles  of  this 
fine  substance  in  all  directions  with  such  velocity,  that  a  particle 
of  light  travels  from  the  sun  to  the  earth  in  8  minutes  13  seconds. 
This  substance  of  light  must  necessarily  be  extremely  attenuated, 
and  not  subject  to  the  action  of  gravity,  consequently  it  must  be 
considered  as  imponderable.  The  difference  of  the  colors  of  light 
rests  upon  the  difference  of  the  velocity  of  transmission ;  reflection 
is,  therefore,  according  to  this  view,  analogous  to  the  rebounding 
of  elastic  bodies.  To  explain  refraction,  according  to  this  theory, 
we  must  assume,  1.  That  there  are,  in  transparent  bodies,  inter- 
stices sufficiently  large  to  allow  of  the  passage  of  particles  of  light ; 
and  2.  That  ponderable  molecules  exert  an  attractive  influence  on 
the  particles  of  light,  and  that  this,  combined  with  the  velocity 
attained  by  the  particles  of  light,  occasions  their  deviation  from 
their  direct  course. 

The  Theory  of  Vibration  assumes,  that  light  is  propagated  by 
the  vibrations  of  an  imponderable  matter  termed  ether.  According 
to  this  theory,  light  is  somewhat  similar  to  sound;  sound,  however, 
is  transmitted  by  the  vibrations  of  a  ponderable  substance,  while 
light  is  propagated  by  the  vibrations  of  an  imponderable  one — 
ether.  This  ether  fills  the  whole  universe,  since  light  penetrates 
the  spaces  of  the  heavens.  This  imponderable  substance  is  not 
only  distributed  through  the  otherwise  vacant  space,  separating 
the  stars,  but  it  penetrates  all  bodies,  filling  up  the  interstices 
occurring  between  ponderable  atoms.  If  the  ether  were  in  a  state 


ELEMENTS   OF   THE   THEORY   OF   UNDULATION.  327 

of  rest  throughout  the  whole  universe,  there  would  everywhere  be 
darkness ;  but  put  into  vibration,  as  it  were,  at  one  spot,  the 
waves  of  light  are  propagated  in  all  directions,  as  the  vibrations 
of  a  chord  are  transmitted  through  a  calm  atmosphere.  Light, 
which  first  arises  from  motion,  is,  therefore,  to  be  distinguished 
from  the  ether  itself,  as  the  vibratory  motion  producing  sound  is 
to  be  distinguished  from  the  vibrating  particles  of  ponderable 
matter. 

For  a  long  time,  both  theories  numbered  adherents  amongst 
eminent  men  of  science.  Newton  established  the  theory  of  ema- 
nation, and  Huyghens  may  be  considered  as  the  founder  of  the 
theory  of  undulation.  The  fundamental  study  of  the  phenomena 
of  light,  which  we  are  about  to  treat  of,  has  afforded  a  decided 
triumph  to  the  theory  of  undulation,  for  these  phenomena  admit 
of  a  very  simple  explanation  by  the  hypothesis  of  air- waves,  but 
not  so  by  the  theory  of  emission. 

Elements  of  the  Theory  of  Undulation. — The  particles  of  a  lumi- 
nous body  vibrate  in  a  manner  similar  to  those  of  sonorous  bodies, 
only  the  undulations  of  light  are  infinitely  more  rapid  than  those 
of  sound  ;  they  are  not,  however,  transmitted  by  ponderable 
matter,  but  by  the  luminous  ether. 

If  a  ray  of  light  be  transmitted  in  the  direction  from  Ji  to  B9 
Fig.  307,  all  the  particles  of  ether  lying  in  a  condition  of  equili- 
brium, upon  the  straight  line  A  JB,  vibrate  in  directions  at  right 

Fig.  307. 


angles  to  Ji  B,  in  almost  the  same  way  as  do  the  parts  of  a  tense 
line,  sharply  struok  at  one  end.  The  curve  in  Fig.  307  repre- 
sents the  mutual  position  of  the  vibrating  molecules  in  a  definite 
moment  of  their  motion. 

Let  us  now  consider  the  vibrations  of  a  molecule  of  ether  some- 
what more  closely.  The  particle  whose  position  of  equilibrium  is 
at  b,  vibrates  continually  between  the  points  V  and  b".  At  V  its 
velocity  is  null ;  the  more,  however,  the  particle  approaches  the 
position  of  equilibrium,  the  more  its  velocity  increases,  until  this 
attains  its  maximum  at  the  moment  in  which  the  molecule  passes 


328          ELEMENTS   OF   THE   THEORY  OF    UNDULATION. 

its  position  of  equilibrium;  from  this  time,  the  velocity  again 
diminishes,  until  it  is  again  null  at  b'f,  on  which  the  motion  begins 
in  an  opposite  direction. 

Although  light  travels  with  extraordinary  rapidity,  its  trans- 
mission is  not  instantaneous ;  the  vibrations  of  a  molecule  of  ether 
are  not,  therefore,  instantaneously  transmitted  in  the  direction  of 
the  ray  to  the  succeeding  molecules.  Let  us  suppose  the  whole 
series  of  molecules  on  the  line  Ji  B  to  be  at  rest.  If  now  the 
molecule  b  begin  its  vibrations  at  a  definite  moment,  all  the  other 
molecules  lying  further  beyond  B  will  begin  to  vibrate  later  in 
proportion  as  they  are  removed  from  b ;  whilst  the  molecule  b 
makes  a  perfect  vibration,  that  is,  whilst  it  moves  from  6'  to  b" 
and  back  again  towards  &',  motion  will  be  transmitted  to  some  one 
molecule,  as  c,  so  that  the  latter  will  begin  its  fresh  vibration  at 
the  same  moment  in  which  b  begins  its  second  motion.  From 
this  time,  the  molecules  b  and  c  will  constantly  be  in  the  same 
phase  of  vibration,  that  is,  they  will  simultaneously  pass  the  posi- 
tion of  equilibrium  moving  towards  the  same  side,  and  will  simul- 
taneously attain  the  maximum  of  deviation  on  either  side  of  A  B. 

The  distance  b  c  between  two  molecules  of  ether  constantly  in 
the  same  phase  of  vibration,  is  termed,  as  we  have  already  seen, 
the  length  of  a  wave.  If  c  d  be  also  the  length  of  a  wave,  the 
molecule  will  begin  its  first  vibration  at  the  moment  in  which  c 
begins  its  secondhand  b  its  third  oscillation;  d  will  from  this 
time  be  constantly  in  the  same  phase  of  vibration  as  c  and  b. 

If  f  lie  half-way  between  b  and  c,  that  is,  if  it  be  removed  half 
the  length  of  a  wave  from  6,  the  molecule  at  f  will  always  be  in 
phases  of  vibration  opposite  to  those  of  the  molecules  at  b  and  c. 
When  b  and  c  attain  the  maximum  of  deviation  above  A  B,f  attains 
the  same  maximum  on  the  opposite  side.  The  molecule  f  passes 
the  position  of  equilibrium  simultaneously  with  b  and  c,  but  moves 
in  an  opposite  direction. 

If  two  molecules  of  ether  be  removed  J  the  length  of  a  wave  from 
each  other  in  the  path  of  a  ray  of  light,  they  will  always  be  affected 
by  equal  but  opposite  velocities.  The  same  applies  to  such  par- 
ticles as  are  removed  f ,  f ,  J,  &c.,  of  the  length  of  a  wave. 

The  length  of  a  wave  is  not  the  same  for  different  colors ;  it 
is  largest  for  the  red,  and  smallest  for  the  violet.  We  cannot 
treat  further  here  of  the  manner  in  which  the  length  of  waves  for 


ELEMENTS   OF   THE   THEORY   OF    UNDULATION.          329 

differently  colored  rays  may  be  determined  with  extraordinary 
accuracy. 

Unequal  periods  of  undulation  and  different  lengths  of  waves 
are  dependent  upon  each  other  •  thus,  the  undulations  of  violet 
rays  are  the  quickest,  and  those  of  the  red  rays  the  slowest. 

We  thus  see  that  in  light  the  difference  of  colors  corresponds 
with  the  unequal  height  and  depth  of  tint. 

We  may  form  a  very  clear  idea  of  the  manner  in  which  waves 
of  light  are  distributed  in  all  directions  from  a  luminous  point,  if, 
as  we  have  already  shown,  we  consider  the  waves  that  arise  upon 
the  surface  of  a  piece  of  still  water  on  the  throwing  in  of  a  stone. 
From  the  spot  where  the  stone  sinks  in  the  water,  circular  waves 
are  formed ;  the  advance  of  these  waves,  from  the  central  point  of 
motion,  does  not  depend  upon  the  separate  particles  of  water  hav- 
ing such  a  progressive  motion,  for,  if  a  light  body,  as  a  piece  of 
wood,  float  upon  it,  within  the  boundary  of  the  undulatory  motion, 
it  will  only  rise  and  fall  alternately.  The  particles  of  water  move 
alternately  up  and  down  at  the  spot  where  the  stone  fell  into  the 
water,  and  this  motion  is  transmitted  in  a  circle  with  equal  velo- 
city; all  the  particles  of  water,  therefore,  which  are  equi-distant 
from  the  middle  point,  will  also  be  in  like  phases  of  vibration ; 
that  is,  they  will  simultaneously  reach  their  highest  and  lowest 
position.  Concentric  wave-elevations  and  depressions  will,  there- 
fore, be  formed,  as  is  shown  in  Fig. 
308.  If,  at  a  definite  moment,  the  com-  Fig.  308. 

plete  circles  correspond  to  the  wave- 
elevations,  and  the  dotted  circles  to  the 
wave-depressions,  the  wave-elevations 
will  spread  outward  in  such  a  manner 
as  to  be,  after  a  short  period  of  time,  ex- 
actly at  the  dotted  axis,  while  the  wave- 
depressions  will  have,  in  like  manner, 
assumed  the  places  defined  by  the  com- 
plete circles. 

All  the  particles  of  water  intervening  between  two  successive 
wave-elevations,  or  wave-depressions,  form  a  wave,  while  the 
length  of  the  wave  is  the  distance  from  one  elevation  to  another, 
or  from  one  depression  to  the  next.  As  one  particle  of  water 
descends  at  a,  for  instance,  from  its  highest  position,  and  then 

28* 


330  INTERFERENCE    OF    RAYS    OF    LIGHT. 

rises  again  to  the  summit  of  a  wave-elevation,  the  latter  will  ad- 
vance one  length  of  a  wave. 

As  the  waves  of  water  distribute  themselves  in  concentric  cir- 
cles around  the  point  of  displacement,  the  undulations  of  light 
move  in  concentric  spherical  layers  around  the  source  of  light ; 
the  surface  of  the  waves  of  light  is  spherical,  at  least,  as  long  as 
the  elasticity  of  the  ether  remains  the  same  in  all  directions. 

Interference  of  Rays  of  Light. — We  will  at  once  proceed  to 
explain  how  the  combined  action  of  two  pencils  of  light  some- 
times produces  increased  light,  and  sometimes  perfect  darkness. 

Such  an  increase  or  cessation  of  light,  produced  by  the  com- 
bined action  of  two  rays  of  light,  is  designated  by  the  term  inter- 
ference of  the  rays  of  light ;  and  may  be  thus  explained. 

In  Fig.  309,  the  lines  Ji  B  and  C  D  represent  two  elementary 

Fig.  309. 


rays  of  light,  which,  emanating  from  one  source,  reach  the  point 
a  by  different  paths,  and  intersect  each  other  at  a  very  acute 
angle.  If  the  distance  traversed  by  the  ray  of  light  C  D  OR  its 
path  from  the  source  of  light  to  the  point  a  be  as  great,  or  1,  2, 
or  3  lengths  of  a  wave  greater  than  the  length  from  the  source  of 
light  to  the  point  a  on  the  path  of  the  other  ray,  the  two  rays  will 
interfere  at  a  in  the  manner  represented  in  Fig.  310. 

The  wave  line  abed  represents,  at  a  given  moment,  the  rela- 
tive position  of  the  particles  of  ether  transmitting  the  rays  in  the 
direction  Jl  B.  The  particle  b  has  just  reached  its  extreme  ex- 
ternal position  below  A  B,  and  the  particle  a  passes  its  point  of 
equilibrium  in  the  direction  indicated  by  the  little  arrow. 

The  dotted  wave  line  shows  us  the  simultaneous  state  of  vibra- 
tion of  the  particles  of  air  propagating  the  pencil  of  light  C  D. 
If  both  rays  have  traversed  equal  distances  from  the  source  of 
light  to  the  point  a,  the  particle  a  will  be  affected  simultaneously 
in  the  same  wray  by  both  rays ;  at  the  moment  represented  in  our 
drawing,  the  particle  a  is  likewise  forced  downward  by  the  second 
wave-  system,  the  intensity  of  vibration  is,  therefore,  twice  as  great 


INTERFERENCE    OF    RAYS    OF    LIGHT.  331 

as  if  its  motion  were  only  influenced  by  the  vibrations  of  one  ray 
of  light. 

In  like  manner  the  vibrations  of  two  rays  of  light  meeting  at 
one  point,  and  deviating  throughout  their  whole  course  about  the 
multiple  of  a  whole  length  of  a  wave,  must  strengthen  each  other. 

Fig.  310  represents  the  combined  action  of  two  rays,  one  of 

Fig.  310. 


which  has  preceded  the  other  by  an  odd  multiple  of  a  half  a  length 
of  a  wave.  By  the  vibrations  of  the  one  ray  (the  wave-line  cor- 
responding to  it  is  fully  delineated,  while  that  of  the  other  ray  is 
only  dotted)  the  particle  a  is  urged  upwards  at  the  same  moment 
in  which  the  undulations  of  the  other  ray  strive  to  move  it  down- 
wards with  equal  force  ;  the  two  opposite  forces,  therefore,  neu- 
tralize each  other,  and  the  particle  a  remains  at  rest. 

We  have  hitherto  only  considered  those  cases  in  which  the  dif- 
ference of  the  interfering  rays  amounts  to  the  multiple  of  a  whole 
length  of  a  wave,  or  to  an  odd  multiple  of  a  half  the  length  of  a 
wave.  If  the  difference  falls  within  these  limits,  an  effect  will  be 
produced  by  the  interference  of  the  two  rays  lying  between  the  lim- 
its of  which  we  have  already  spoken,  that  is,  there  can  neither  be 
any  complete  destruction  of  the  undulation,  nor  any  doubling  of 
the  intensity  of  the  undulation.  The  actual  intensity  of  undula- 
tion produced,  approaches  more  to  one  or  other  of  these  limiting 
values,  according  as  the  difference  of  the  path  approximates  more 
nearly  to  an  odd  multiple  of  a  half  a  wave,  or  to  a  multiple  of 
the  whole  length  of  a  wave. 

We  now  pass  to  the  consideration  of  those  phenomena  which 
admit  of  being  referred  to  the  principle  of  interferences. 

Refrangibility  of  Light. — If  we  look  at  a  little  solar-image  on 
the  inside  of  a  blackened  watch-glass,  a  polished  metal  button,  or 
a  thermometer  bulb,  by  means  of  a  fine  circular  opening,  as  may 
be  made  with  a  fine  needle  in  a  card,  we  see  a  light  round  spot 
surrounded  by  several  colored  rings.  Fig.  312  represents  this 
phenomenon. 

If,  instead  of  the  point,  we  make  a  fine  straight  slit  in  the  card, 


332 


REFRANGIBILITY    OF    LIGHT. 


and  look  through  it  at  the  solar  image  upon  the  watch-glass,  or 
(what  is  better)  upon  the  light  line  on  a  glass  tube  blackened  in 


Fig.  311. 


Fig.  312. 


the  inside,  and  laid  in  the  sun,  we  shall  see  the  phenomenon  ex- 
hibited at  Fig.  311.  In  the  centre  of  the  image  we  shall  see  a 
light  stripe,  having  at  both  sides  narrower  colored  stripes,  which 
have  a  less  intensity  of  light  as  they  approach  the  outside. 

The  finer  the  circular  opening,  and  the  narrower  the  slit,  the 
broader  will  be  the  rings  or  the  stripes,  as  the  case  may  be. 

The  simplest  mode  of  observing  this  phenomenon  is  by  holding 
a  glass  of  only  one  color,  a  red  one  for  instance,  to  the  eye  with 
the  card;  then,  on  looking  through  the  slit,  we  shall  see  in  the 
centre  a  bright  red  stripe  bounded  on  both  sides  by  a  black  stripe ; 
on  either  side  there  will  then  succeed  several  red  lateral  images 
which  always  become  fainter,  the  one  being  divided  from  the  other 
by  a  black  stripe,  nearly  in  the  manner  represented  in  the  under- 
most series  in  Fig.  315. 

The  bright  sides  as  well  as  the  bright  stripe  form  the  same 
color  in  the  middle ;  they  are  not  sharply  defined  by  the  black 
stripes ;  the  transition  from  clear  light  to  the  darkest  spots  is, 
therefore,  gradual. 

We  see  the  same  phenomenon  through  a  green  glass,  only  in 
this  case,  the  stripes  are  narrower,  and  when  a  violet  glass  is  used 
they  are  still  more  so,  as  indicated  in  Fig.  313.  The  explanation 

of  these  phenomena  can  be 
here  only  cursorily  touched 
upon. 

If  the  light  fall  from  a 
sufficiently  remote  point, 
straight  upon  the  plane  of 
the  screen  Jl  B  in  which 
there  is  the  opening  C  D, 


Fig.  313. 


REFRANGIBILITY    OF    LIGHT. 


333 


we  may  consider  all  the  particles  of  ether  at  this  opening  as 

equally  remote  from  the  source  of  light, 

and,  therefore,  in  like  phases  of  vibra- 

tion.    But  each  one  of  these  particles 

of  ether  transmits  its  vibrations  on  the 

further  side  of  the  screen  in  all  direc- 

tions, as  if  it  were  a  self-luminous  par- 

ticle ;  the  intensity  of  the  light  at  any 

one  point  s9  lying  behind  the  screen, 

depends  consequently,  upon  the  action 

produced   by  the   interference   of  all 

the  rays  emanating  from  the  different 

points  of  the  opening  C  D,  and  meeting  at  s. 

The  rays  of  light  which  are  transmitted  from  C  Z),  at  right 
angles  to  the  opening,  will  always  strengthen  each  other ;  conse- 
quently the  centre  of  the  image  will  be  bright.  If,  however,  we 
pass  over  to  points  lying  at  the  side,  the  rays  meeting  here,  will 
not  strengthen  each  other;  the  intensity  of  light  must,  therefore, 
diminish  laterally  towards  a  point  at  which  all  the  rays  coming 
from  C  D,  and  meeting  here,  will  entirely  destroy  each  other ;  here 
we  shall  observe  a  dark  stripe. 

Still  further  from  the  centre,  there  are  again  points  at  which  no 
complete  destruction  of  the  waves  proceeding  from  CD,  and  meet- 
ing here,  occurs,  where,  consequently,  light  is  again  observed ;  to 
this  succeed  darker  stripes,  by  which  all  the  waves  of  light  perfectly 
destroy  each  other.  The  reason  of  the  light  and  dark  stripes  not 
coinciding  in  the  differently  colored  rays,  depends  upon  the  differ- 
ence of  the  lengths  of  their  waves. 

When  all  the  differently  colored  rays  combine,  when,  for  in- 
stance, we  look  at  the  white  solar  image  through  a  fine  aperture, 
without  the  assistance  of  a  glass,  we  shall  see  a  white  streak  in 
the  centre,  because  here  the  maximum  of  the  intensity  of  light  for 
all  colors  is  found;  but  the  side  images  are  all  colored,  there  being 
nowhere  a  perfectly  white  or  perfectly  black  stripe  to  be  seen,  for, 
where  there  is  a  black  stripe  for  one  color,  there  will  be  a  light 
stripe  for  other  colors. 

We  have  here  only  slightly  touched  upon  the  explanations  ne- 
cessary to  elucidate  the  phenomena  of  refrangibility,  since  a  fuller 
exposition  of  the  question  would  carry  us  beyond  our  limits. 

The  form  of  the  phenomena  of  refrangibility  depends  upon  the 


334  REFRANGIBILITY   OF    LIGHT. 

form  of  the  apertures ;  and  also  changes  with  the  number  of  the 
latter. 

If  two  minute  circular  apertures  in  a  screen  lie  near  each  other, 
as  thus  4 ,,  we  shall  again  see,  on  looking  towards  a  luminous  point, 
the  same  rings  (Fig.  312)  as  if  there  were  only  one  aperture ;  these 
rings  appear,  however,  to  be  intersected  by  straight  black  stripes 
lying  at  right  angles  to  the  direction  of  the  line  uniting  both 
openings.  These  black  stripes  also  pass  through  the  central  light 
spot,  Fig.  312. 

This  experiment  clearly  shows,  that  darkness  may  arise  from  the 
combination  of  two  rays  of  light,  or,  in  other  words,  that  the  action 
of  one  ray  of  light  may  be  destroyed  by  that  of  another.  If  the 
light  enter  only  through  one  hole,  we  shall  see  the  figure  repre- 
sented in  Fig.  312;  as  soon,  however,  as  a  second  aperture  is 
added,  black  stripes  will  appear  in  the  bright  parts  of  this  image ; 
here,  therefore,  the  action  of  light  produced  by  rays  incident  at 
one  aperture,  will  be  destroyed  by  that  of  the  rays  passing  through 
the  other  aperture. 

Very  curious  phenomena  are  observed  in  suffering  white  light 
to  pass  through  a  wire  gauze — this  is  exemplified  in  the  frontis- 
piece in  Fig.  1,  Plate  I.  In  the  centre  appears  the  direct  image 
of  the  line  of  light ;  it  is  white,  owing  to  the  combination  of  the 
maxima  of  all  the  colors.  On  either  side  of  this  line  of  light  are 
dark  spaces,  to  which  succeeds  a  colored  band  similar  to  the 
prismatic  spectrum,  whose  violet  extremity  is  turned  inwards. 
After  a  second  totally  dark  space  comes  another  broad  colored 
band,  the  red  extremity  of  which  touches  upon  the  violet  extremity 
of  a  third  colored  band. 

Fig.  2,  Plate  I,  also  exhibits  the  phenomenon  observed  through 
simple  gratings,  when  two  of  these  are  crossed  before  the  object- 
glass  of  a  telescope,  while  we  direct  it  towards  a  luminous  point. 
The  middle  is  occupied  by  the  white  image  of  the  luminous  point, 
while  around  are  a  number  of  prismatic  images,  which  all  turn 
their  violet  extremities  inward. 

Very  beautiful  phenomena  of  refrangibility  are  manifested  as 
seen  through  a  series  of  fine  apertures,  as,  through  a  row  of  fine 
parallel  lines  scratched  upon  a  glass  plate.  To  this  class  belong 
the  phenomena  seen  on  looking  towards  a  luminous  point  through 
the  feather  of  one  of  the  smaller  kinds  of  birds ;  the  flame  of  a 
taper  suffices  to  show  this  with  great  brilliancy. 


COLORS    OF    THIN   PLATES. 


335 


Fig.  315. 


If  we  strew  lycopodium  seed  upon  a  glass  plate,  and  look  through 
it  towards  a  lighted  taper,  we  shall  see  a  beautiful  areolar  figure, 
composed  of  many  colored  rings.  This  is  also  a  phenomenon  of 
refrangibility. 

Colors  of  thin  Plates.— Every  transparent  body  appears  vividly 
colored,  if  seen  in  sufficiently  thin  plates,  as  is  well  exhibited  in 
soap-bubbles.  The  thin  pieces  of  a  glass  sphere  expanded  to 
bursting,  before  the  glass-blower's  lamp,  exhibit  the  most  dazzling 
colors;  similar  colors  are  observed  when  a  drop  of  oil  (as  oil  of 
turpentine)  is  spread  over  a  surface  of  water ;  or,  when  a  glitter- 
ing piece  of  metal,  heated  in  the  fire,  is  gradually  covered  with 
a  coating  of  oxide  (in  the  annealing  of  steel).  Thin  layers  of  air 
produce  such  colors  as  these,  as  may  be  often  seen  in  the  flaws  in 
somewhat  thick  masses  of  glass. 

These  colors  are  exhibited  with  the  greatest  regularity  in  the 
form  of  rings,*  if  we  lay  a  glass 
lens  of  great  focal  length  upon  a 
plate  of  glass,  or  the  plate  of  glass 
upon  the  lens.  Newton,  who  ob- 
served these  colored  rings,  which 
are  commonly  termed  Newton's 
rings,  used  lenses  whose  radii  of 
curvature  amounted  from  15  to  20 
yards.  Where  the  plate  of  glass 
touches  the  lens,  we  see,  by  re- 
flected light,  a  black  spot  sur- 
rounded with  colored  concentric 
rings,  becoming  narrower  and  fainter  towards  the  outer  edges,  as 
seen  in  Fig.  315. 

If  we  look  at  the  rings  through  a  monochromatic  glass,  we 
only  see,  alternately,  bright  and  dark  rings.  These  rings  are 
broader  for  red  than  for  green  light,  and  narrower  for  violet  than 
for  green.  If,  instead  of  colored,  we  use  white  light,  we  shall  not 
be  able  to  see  a  thoroughly  white,  or  a  thoroughly  black  ring, 
because  neither  the  light  nor  the  dark  rings  of  the  different  colors 


*  The  ring  system  is  most  beautifully  exhibited  in  several  uni-  and  bi-axal  crys- 
tals, and  for  the  sake  of  more  striking  illustration  of  these  phenomena,  we  have 
given  colored  representations  of  the  appearances  manifested,  which  will  be  found 
in  Plate  II. 


336  COLORS  OF  THIN  PLATES. 

coincide ;  we  see  colors  throughout,  which,  instead  of  being  the 
pure  hues  of  the  spectrum,  are  mixed  colors. 

These  phenomena  of  color  may  be  explained  in  the  following 
manner: 

If  rays  of  light  fall  upon  any  lamina  of  a  transparent  body,  they 
will  be  reflected  partially  at  its  upper,  and  partially  at  its  lower, 
surface ;  and  the  rays  of  light  reflected  from  the  two  surfaces  will 
interfere,  either  destroying  or  strengthening  each  other,  according 
to  the  difference  of  the  paths  which  they  have  traversed. 

Let  us  consider  this  more  closely.  In  Fig.  316,  M  N  OP 
represents  a  thin  lamina  of  a  transparent 
body,  on  which  a  pencil  of  parallel  rays 
a  b  impinges ;  this  pencil  of  rays  will  be 
partially  reflected  in  the  direction  b  c,  and 
partially  refracted  towards  d.  But  the 
refracted  rays  will  suffer  a  second  separa- 
tion at  the  surface  0  P ;  the  reflected  por- 
tion will  emerge  at  e,  in  the  same  direc- 
/  tion  as  the  pencil  of  light  reflected  at  the 

first  surface  M  JV;  consequently  both  pen- 
cils of  light,  b  c  and  ef  will  interfere. 

But  how  happens  it,  that  only  thin  lamina  exhibit  such  colors 
as  these,  while  plates  of  some  thickness  do  not  manifest  them  ? 
Let  us,  for  the  sake  of  more  easy  concession,  assume  that  the 
waves  of  light  in  violet  rays  are  half  as  great  as  those  in  red 
rays  (they  are  actually  somewhat  beyond  half  as  great);  then  the 
diameter  of  the  violet  rings  will  be  the  half  of  that  of  the  red 
rings;  at  the  place  where  the  first  dark  ring  for  red  light  is 
situated,  there  will  be  also  the  second  dark  ring  for  violet  light, 
and  one  light  ring  for  a  color  lying  nearly  in  the  middle  between 
the  red  and  the  violet;  this  color  is  decidedly  predominant  at  this 
spot. 

Where  the  seventh  dark  ring  for  red  light  occurs,  there  will 
be  the  fourteenth  dark  ring  for  violet  light ;  at  this  spot,  there 
will,  therefore,  still  be  six  dark  rings,  and  seven  bright  rings  for 
the  intermediate  colors.  If,  therefore,  the  extreme  red,  the 
boundary  between  red  and  orange,  between  orange  and  yellow, 
yellow  and  green,  green  and  blue,  blue  and  indigo,  indigo  and 
violet,  and  the  extreme  violet,  be  at  the  minimum,  the  interme- 
diate rays  of  red,  orange,  yellow,  green,  blue,  indigo,  and  violet, 


POLARIZATION    OF    LIGHT. 


337 


Fig.  317. 


will  be  at  the  maximum ;  no  one  of  these  colors  can,  therefore, 
predominate,  and  combined  they  will  yield  white. 

By  transmitted  light,  thin  plates  also  show  similar,  but  far 
fainter  colors,  which  are  complementary  to  those  exhibited  by 
reflected  light. 

Polarization  of  Light. — If  we  cut  from  a  transparent  crystal 
of  tourmaline,  a  plate  whose  surface  runs  parallel  to  the  principal 
axis,  and  if  we  look  through  it  towards  a  polished  plate  reflecting 
the  light  of  the  sky  towards  the  eye  at  an  angle  of  from  30°  to 
40°,  the  polished  surface  will  appear  bright  or  dark,  according 
as  we  turn  the  section  of  the  tourmaline ;  it  will  not,  therefore,  in 
every  position,  suffer  the  transmission  of  the  rays  reflected  from 
the  plate.  The  pencil  of  light  must,  therefore,  by  its  reflection 
from  the  polished  plate,  have  undergone  a  peculiar  modification, 
which  we  designate  by  the  term  polarization. 

If  we  had,  under  similar  circum- 
stances, examined  the  rays  reflected 
from  the  glass  plate  with  the  plate  of 
tourmaline,  we  should  have  observed 
the  same  phenomenon ;  consequently 
rays  of  light  are  polarized  by  reflection 
from  a  glass  surface. 

The  tourmaline  plate  maybe  replaced 
by  a  glass  mirror. 

If  an  ordinary  ray  of  light  a  b  fall 
upon  a  plane  glass  plate  /  g  h  i  at  an 
angle  of  35°  25',  it,  for  the  most  part, 
becomes  reflected  in  the  direction  b  c, 
according  to  the  usual  laws.  The  ray  reflected  in  the  direction 
b  c,  is  now  polarized  by  this  reflection.  These  phenomena  can  be 
best  observed  when  the  mirror  fg  h  i  is  blackened  on  the  reverse 
side,  for  besides  the  rays  polarized  by  reflection,  some  coming 
from  objects  under  the  mirror  are  also  transmitted  in  the  direc- 
tion b  c,  and  which  have  passed  through  it. 

If  the  ray  b  c,  polarized  by  reflection,  fall  upon  a  second  glass 
plate,  likewise  blackened  upon  the  reverse  side,  and  parallel  to 
the  under  one,  the  ray  b  c  will  also  make  an  angle  with  it  of  35°, 
and  the  plane  of  reflection  of  the  upper  mirror  will  coincide  with 
that  of  the  lower  one.  In  this  position  of  the  second  mirror,  the 
ray  b  c  is  reflected  like  every  ordinary  ray  of  light ;  if,  however, 
29 


338  POLARIZATION    OF    LIGHT. 

we  turn  the  upper  mirror  in  such  a  manner  that  the  direction  of 
the  ray  b  c  forms  the  axis  of  rotation,  the  angle  made  by  the 
incident  ray  b  c  with  the  plane  of  the  mirror  will  remain  the  same, 
but  the  parallelism  of  the  two  mirrors  will  cease,  and  the  plane  of 
reflection  of  the  upper  mirror  will  no  longer  coincide  with  that  of 
the  lower.  If,  now,  we  turn  the  upper  mirror  from  its  position  of 
parallelism  with  respect  to  the  other  mirror,  the  intensity  of  the 
twice  reflected  rays  will  diminish  the  more  the  angle  which  is 
made  by  the  plane  of  reflection  of  the  upper  mirror  with  that 
of  the  lower  increases,  until  it  becomes  90°,  or,  in  other  words, 
until  the  planes  of  reflection  of  both  mirrors  are  at  right  angles 
to  each  other.  In  this  position  the  ray  b  c  will  no  longer  be  re- 
flected from  the  upper  mirror,  as  would  be  the  case  if  b  c  were  an 
ordinary  ray  of  light.  By  the  continued  turning  of  the  upper 
mirror,  the  intensity  of  the  reflected  ray  gradually  increases,  until 
it  again  attains  its  maximum  on  the  rotation  amounting  to  180°. 
In  this  position  the  planes  of  reflection  of  the  two  mirrors  will 
again  coincide.  If  we  turn  it  still  further,  the  ray  reflected  to  the 
upper  mirror  will  again  become  fainter,  disappearing  entirely 
when  the  planes  of  reflection  of  both  mirrors  again  cross  each 
other,  consequently  when  the  rotation  amounts  to  270°,  &c. 

An  arrangement  by  which  two  such  mirrors  can  be  used,  and 
by  which  the  above  described  experiments  maybe  made,  is  termed 
a  polarizing  apparatus.  The  simplest  arrangement  that  can  be 
adopted,  is  the  following :  A  mirror  blackened  at  the  back  is  so 
fastened  to  one  end  of  a  metallic  or  wooden  tube,  that  it  makes 
an  angle  of  35°  with  the  axis  of  the  tube,  when  all  the  rays, 
incident  on  the  mirror  at  an  angle  of  35°,  are  so  reflected  that 
they  pass  through  the  tube  in  the  direction  of  this  axis.  At  the 
other  end  of  the  tube  there  is  a  ring,  whose  axis  corresponds  with 
that  of  the  tube,  and  which  therefore  admits  of  being  turned  round 
upon  a  plane,  at  right  angles  to  this  axis.  To  this  ring  is  fastened 
a  second  mirror,  blackened  in  like  manner  as  the  other,  and  also 
making  an  angle  of  35°  with  the  axis  of  the  tube.  By  turning  the 
ring,  the  mirror  is  made  to  revolve  with  it,  and  may  thus  be 
brought  into  all  the  positions  we  have  just  mentioned. 

Such  a  polarizing  apparatus  is,  however,  very  inconvenient ; 
and  that  delineated  in  Fig.  318,  and  represented  at  one-fourth 
of  its  natural  size,  is  far  better  in  every  respect.  Two  rods  are 
inserted  diametrically  opposite  to  each  other,  in  the  rim  of  a 


POLARIZATION   OF   LIGHT. 


339 


Fig.  318. 


stand,  which  must  be  made  sufficiently  heavy  to  give  the  whole 

the  stability  necessary  to  support 

the  apparatus  ;  between  these  rods 

there  is  a  frame  A  B,  enclosing  a 

polished  glass  mirror.    This  frame, 

together  with  the  mirror,  may  be 

made   to   revolve   in  a  horizontal 

axis  by  means  of  a  pivot,  by  which 

means  the  glass  may  be  moved  at 

will,  in  any  position  about  the  direc- 
tion of  the  perpendicular.  The  mir- 
ror is  generally,  however,  placed 

in   such  a  position  that  its  plane 

shall  make  an  angle  of  35°  with 

the  vertical.     If,  in  this  position  of 

the  mirror,  a  ray  of  light  a  b  falls 

upon   it    at   an  angle   of  35°,    it 

passes  partially  through  the  glass, 

(but  of  this  we  need  not  take  any 

account,)  and  is  partially  reflected 
vertically  downwards  in  the  direc- 
tion b  c.  This  reflected  ray  is  now 
polarized,  and  a  vertical  plane  pass- 
ing through  the  lines  a  b  and  b  c, 
is  its  plane  of  polarization. 

At  the  base  of  the  apparatus  there  is  a  common  mirror,  black- 
ened beneath,  and  horizontally  placed,  on  which  the  polarized 
rays  b  c  impinge  rectangularly ;  this  ray  is,  therefore,  reflected  in 
the  same  direction  in  which  it  came,  and  passing  through  the 
polarizing  mirror  proceeds,  in  a  vertical  direction,  to  the  upper 
part  of  the  apparatus.  The  upper  extremities  of  the  columns  (we 
will  not  at  present  treat  of  the  middle  part  of  the  apparatus),  have 
a  graduated  ring.  The  zero  of  this  division  is  so  situated  that  if 
we  imagine  a  vertical  plane  drawn  through  0  and  180°,  it  will 
coincide  with  the  plane  of  reflection  of  the  lower  mirror,  and  con- 
sequently with  the  plane  of  polarization  of  the  rays  polarized  by 
it.  Within  this  graduated  ring,  there  is  another  that  can  be  made 
to  revolve,  and  on  which  are  placed  two  columns,  diametrically 
opposite  to  each  other,  having  between  them  a  mirror  of  black 
glass,  or  a  mirror  blackened  on  the  back,  which  is  fastened  in  the 


340  POLARIZATION   OF   LIGHT. 

same  manner  as  the  lower  polarizing  mirror ;  as  the  lower  one  is 
made  to  revolve  round  a  horizontal  axis,  the  blackened  mirror 
may  easily  be  so  placed  as  to  make  an  angle  of  35°  25'  with  the 
vertical. 

The  revolving  ring  on  which  the  columns  stand,  slopes  some- 
what at  the  edges,  while,  in  the  centre  of  the  anterior  half  of  the 
ring,  an  index  is  drawn  upon  the  slope.  A  vertical  plane  passing 
through  this  index  to  the  middle  point  of  the  ring,  coincides  with 
the  plane  of  the  reflection  of  the  blackened  mirror.  If  we  turn 
the  ring  bearing  the  upper  mirror,  so  that  the  index  coincides 
with  the  0  of  the  graduated  lines,  the  planes  of  reflection  of  the 
upper  and  lower  mirror  will  coincide.  The  same  will  be  the 
case  when  the  index  stands  at  180°.  If  the  index  stand  at  90°, 
as  in  our  figure,  or  at  270°,  the  plane  of  reflection  of  the  upper 
mirror  will  form  a  right  angle  with  the  plane  of  reflection  of  the 
lower  mirror. 

The  phenomena  of  ordinary  polarization,  which  may  be  observed 
by  this  apparatus,  are  as  follows.  If  both  mirrors  lie  parallel  to 
each  other,  if,  therefore,  the  index  of  the  ring  bearing  the  black 
glass,  stand  at  0°,  the  upper  mirror  will  reflect  the  rays  impinging 
upon  it  from  below,  and  the  field  of  vision  will  appear  conse- 
quently clear.  If  we  turn  the  analyzing  mirror  (this  is  the  com- 
mon term  for  the  upper  mirror)  from  its  position,  the  intensity  of 
the  light  reflected  by  it  will  diminish  more  and  more,  until  it 
comes  at  last  to  0,  when  the  index  will  stand  at  90°.  In  this 
position,  therefore,  the  blackened  mirror  no  longer  reflects  the 
rays  impinging  upon  it  from  below,  and  the  field  of  vision  appears 
dark.  If  we  turn  it  still  further,  it  becomes  gradually  lighter, 
and,  when  the  index  stands  at  180°,  the  intensity  of  the  light  is 
again  equal  to  what  was  observed  at  0°.  The  light,  however, 
diminishes  again  when  we  turn  the  mirror  beyond  180°,  and  the 
field  of  vision  becomes  a  second  time  dark  when  the  index  stands 
at  270°. 

It  is,  of  course,  evident  that,  during  this  rotation,  the  direction 
of  the  blackened  mirror  must  remain  unchanged  with  respect  to 
the  vertical.  But,  in  all  positions,  the  upper  mirror  makes  an 
angle  of  35°  25'  with  the  vertical.  If,  without  altering  any- 
thing else  in  the  apparatus,  we  change  the  position  of  the  lower 
mirror  with  regard  to  the  incident  rays,  if,  for  instance,  we  place 
it  so  as  to  make  an  angle  of  25°  with  the  vertical,  those  rays  will 


POLARIZATION   OF   LIGHT.  341 

reach  the  upper  mirror  of  the  apparatus  which  have  made  an  angle 
with  the  lower  mirror.  If  we  repeat  the  above  experiment,  we 
shall  find  that  the  light  reflected  from  the  upper  mirror  is  never 
quite  null.  If  the  upper  mirror  be  so  placed  that  its  plane  of 
reflection  cross  that  of  the  lower  one,  if,  therefore,  the  index  of  the 
lower  division  stand  at  90°,  although  less  light  will  be  reflected  in 
this  position  than  in  any  other,  still,  some  portion  of  the  rays 
coming  from  below,  will  be  reflected. 

We  may  conclude  from  this,  that  the  rays  reflected  from  the 
lower  mirror  are  only  partially  polarized  at  an  angle  of  25°.  The 
more  the  angle,  which  the  rays  incident  upon  the  lower  glass  mirror 
make  with  its  plane,  deviates  from  35°  25',  the  more  imperfect  is 
the  polarization.  The  angle  at  which  perfect  polarization  takes 
place  (viz.  35°  25'  for  glass),  is  termed  the  angle  of  polarization. 
Metallic  surfaces  have  not  the  property  of  polarizing  light  by  re- 
flection ;  we  cannot,  therefore,  use  mirrors  plated  on  the  back  with 
tin  and  quicksilver  for  experiments  in  polarization. 

The  polarization  of  light  is  explained  according  to  the  undula- 
tory  theory,  on  the  hypothesis  that  all  the  undulations  of  a  polar- 
ized ray  of  light  occur  in  one  and  the  same  plane,  whilst  the 
undulations  of  an  ordinary  ray  of  light  take  place  in  ftvery  possi- 
ble line,  at  right  angles  to  its  direction. 

Double  Refraction. — If  we  place  a  rhombohedron  of  Iceland  spar 
upon  a  piece  of  paper,  on  which  a  black  point  or  line  has  been 
drawn,  we  shall  see  this  point  or  line  double.  If  we  form  a  prism 
of  this  spar,  we  shall  see  a  double  image  of  every  object  looked  at. 
This  experiment  proves  that  every  ray  of  light  impinging  on  a 
prism  of  Iceland  spar  is  divided  into  two  portions,  which  do  not 
obey  the  same  laws  of  refraction,  and  that  this  spar  has  the  pro- 
perty of  double  refraction. 

If  we  examine  through  a  plate  of  tourmaline  the  two  objects 
seen  by  means  of  the  Iceland  spar,  we  shall  find  that  both  rays  are 
polarized,  for  according  as  we  turn  the  plate  of  tourmaline,  one  or 
other  of  the  images  will  disappear;  the  plane  in  which  the  parti- 
cles of  one  ray  vibrate  is  at  right  angles  to  the  plane  of  vibration 
of  that  of  the  other  ray. 

Iceland  spar  is  not  the  only  doubly  refracting  body;  this  pro- 
perty belongs  to  all  crystalizable  substances  not  belonging  to 
regular  systems  of  crystalization. 

In  every  doubly  refracting  crystal,  there  are  one  or  two  direc- 

29* 


342  POLARIZATION   OP   LIGHT. 

tions  in  which  double  refraction  does  not  take  place ;  these  direc- 
tions are  termed  the  optical  axes. 

A  development  of  the  laws  of  double  refraction  would  lead  us 
beyond  our  limits.  If  we  lay  a  very  thin  plate  of  crystalized 
gypsum  upon  the  middle  circle  of  the  polarizing  apparatus,  seen 
in  Fig.  318,  it  will  appear  colored,  changing  (other  circumstances 
remaining  the  same)  its  color  with  the  thickness  of  the  plate. 

If  a  thin  plate,  when  laid  between  mirrors,  crossing  each  other, 
shows  a  definite  color,  the  color  complementary  to  it  will  appear 
when  these  mirrors  are  parallel. 

These  phenomena  of  color  arise  from  the  two  rays  into  which 
the  incident  light  is  separated  (for  crystals  of  gypsum  are  doubly 
refracting)  traversing  the  plate  with  equal  velocity,  and  interfer- 
ing after  reflection  from  the  upper  mirror. 

Plates  of  other  crystals  exhibit  similar  colors  when  made  suffi- 
ciently thin. 

If  we  cut  a  plate  from  a  doubly  refracting  crystal,  whose  surface 
is  at  right  angles  to  the  optical  axis,  it  will  show,  when  brought 
into  the  polarizing  apparatus,  or  laid  between  the  plates  of  tour- 
maline, very  beautifully  colored  rings,  the  formation  of  which 
may  be  explained  in  the  same  way  as  the  colors  of  the  plates  of 
gypsum. 


CHEMICAL    ACTION    OF    LIGHT.  343 


CHAPTER  VI. 

CHEMICAL  ACTIONS  OF  LIGHT. 


Influence  of  Light  on  Chemical  Combinations  and  on  Decomposi- 
tions.— At  an  ordinary  temperature,  chlorine  and  hydrogen  gases 
do  not  combine  with  each  other  in  the  dark;  but  as  soon  as  we 
give  admittance  to  light,  the  combination  takes  place,  slowly  by 
simple  daylight,  but  is  accompanied  with  an  explosion  when  ex- 
posed to  the  direct  rays  of  the  sun.  Chlorine,  absorbed  by  water, 
has  the  power  of  gradually  withdrawing  the  hydrogen  from  it 
only  when  exposed  to  the  action  of  light ;  phosphorus,  kept  in 
water,  is  converted,  when  exposed  to  the  sun,  into  the  red  oxide  of 
phosphorus.  At  ordinary  temperatures,  concentrated  nitric  acid 
is  partially  decomposed  by  light  into  oxygen  and  nitrous  acid ; 
white  chloride  of  silver  becomes  first  colored  violet  by  the  action 
of  light,  and  subsequently  quite  black,  and  a  portion  of  the  chlo- 
rine escapes,  &c.  These  are  only  a  few  of  the  most  striking 
instances  adduced  to  show  the  influence  of  light  upon  chemical 
combinations  and  upoj|  decomposition,  and  all  chemical  treatises 
afford  numerous  examples  of  the  same  thing. 

The  influence  of  light  upon  the  decomposition  of  organic  sub- 
stances is  very  remarkable ;  for  instance,  it  promotes  the  union  of 
the  oxygen  of  the  atmosphere  with  the  carbon  and  hydrogen  of 
organic  substances ;  hence,  arises  the  fading  of  vegetable  coloring 
matter  in  light,  especially  in  sunlight ;  the  yellow  coloration  of  oil 
of  turpentine,  and  the  green  hue  of  yellow  guaiacum,  on  exposing 
to  light  a  piece  of  paper,  dipped  in  a  spirituous  solution  of  thin 
gum,  resin,  &c.  Light  is  absolutely  necessary  to  the  vigorous 
growth  of  living  plants,  their  perfect  development  being  impossi- 
ble in  the  dark,  where  they  soon  acquire  a  sickly  appearance,  and 
their  leaves  and  blossoms  grow  pale.  Plants,  reared  in  a  room,, 
always  incline  towards  the  windows.  The  green  portions  of 


344  PHOTOGRAPHY. 

plants  absorb  carbonic  acid  from  the  air;  this  carbonic  acid  is 
decomposed,  the  carbon  remaining  as  a  constituent  of  the  plants, 
whilst  the  oxygen  is  again  given  off  to  the  atmosphere.  This 
decomposition  of  carbonic  acid,  and  exhalation  of  oxygen,  into  the 
air,  take  place  only  under  the  influence  of  light.  We  may  easily 
convince  ourselves  of  this  fact,  by  laying  a  fresh  green  twig  under 
a  glass  bell,  filled  with  water,  holding  in  solution  carbonic  acid ; 
in  the  light,  numerous  gas  bubbles  develop  themselves  upon  the 
leaves,  and  rise  in  the  upper  part  of  the  glass  bell ;  the  gas,  thus 
collected,  is  carbonic  acid  gas.  This  development  of  gas  does 
not  take  place  in  the  dark,  and  ceases  as  soon  as  all  free  carbonic 
acid  is  removed  from  the  water. 

The  chemical  actions  of  the  blue  and  violet  rays  are  generally 
much  stronger  than  those  of  the  red. 

Photography. — The  idea  first  occurred  to  Wedgwood  to  avail 
himself  of  the  blackening  of  chloride  of  silver  to  fix  the  pictures 
of  the  Camera  Obscura,  and  Davy  obtained  the  images  of  small 
objects  on  chloride  of  silver  paper,  by  means  of  a  solar  microscope ; 
but  these  were  soon  effaced  by  the  continuous  action  of  light 
upon  the  chloride  of  silver.  JViepce  advanced  the  art  of  fixing 
these  photographic  images ;  but  it  remained  for  Daguerre  to  dis- 
cover, after  many  careful  and  laborious  attempts,  a  method  by 
which  almost  incredible  results  are  attained. 

The  substance  on  which  Daguerre's  photographic  images  are 
represented,  is  a  copper  plate  thinly  covered  with  silver.  After 
being  sufficiently  purified,  this  plate  is  laid  over  a  square  porce- 
lain dish,  filled  with  an  aqueous  solution  o^chloride  of  iodine,  and 
exposed  to  the  vapor  of  the  iodine,  until  a  goldish  yellow,  or  a 
violet  layer  of  iodide  of  silver  is  formed  upon  the  surface.  The 
plate  is  now  put  into  the  Camera  Obscura,  being  carefully  kept 
from  the  light  during  its  removal,  exactly  at  the  place  where  a 
well  defined  image  of  the  object  to  be  delineated  appears.  After 
a  certain  time,  the  duration  of  which  depends  upon  various  cir- 
cumstances, the  plate  is  removed  from  the  Camera  Obscura.  There 
is  now  no  trace  of  an  image  to  be  perceived,  this  appearing  only 
on  bringing  the  plate  over  a  metallic  plate  somewhat  warmed,  and 
covered  with  a  thin  layer  of  mercury.  As  soon  as  the  image  is 
sufficiently  well  defined,  the  plate  is  placed  in  a  solution  of  hypo- 
sulphate  of  soda,  or  in  default  of  this,  in  a  boiling  solution  of 


PHOTOGRAPHY.  345 

chloride  of  sodium,  by  which  the  coating  of  iodide  of  silver  is 
dissolved,  and  all  further  action  of  light  prevented. 

Light  acts  on  those  parts  of  the  iodized  plate  on  which  the  light 
portions  of  the  picture  in  the  Camera  Obscura  have  fallen  before 
the  action  becomes  apparent  to  the  eye ;  thus  the  portions  of  the 
plate  which  are  most  exposed  to  light  have  acquired  the  property 
of  condensing  the  vapor  of  mercury;  here,  therefore,  the  mercury 
is  precipitated  in  infinitely  minute  globules,  whilst  no  such  pre- 
cipitate occurs  where  the  light  has  not  acted.  After  the  unchanged 
iodide  of  silver  has  been  entirely  washed  away  from  the  last 
named  parts,  we  have  a  fine  coating  of  the  precipitate  on  the 
light  portions,  while,  where  the  light  does  not  act,  the  shining 
silvered  surface  appears;  and  if  we  hold  the  plate  in  such  a  man- 
ner that  the  mirror  reflects  to  the  eye  the  ray  coming  from  dark 
objects,  this  silvered  surface  forms  the  dark  back-ground,  on  which 
the  light  parts  are  produced  by  the  light  scattered  in  all  directions 
from  the  globules  of  mercury. 

If  we  leave  the  plate  too  long  in  the  Camera  Obscura,  the  action 
of  the  light  becomes  apparent  upon  the  iodized  plate,  whilst  the 
iodide  of  silver  is  blackened  in  those  parts  where  the  light  acts  most 
strongly ;  the  picture  thus  produced  is  a  negative  picture,  that  is 
to  say,  the  light  parts  of  the  object  correspond  to  the  dark  por- 
tions of  the  image,  and  vice  versa.  If  we  leave  the  plate  in  the 
Camera  Obscura  until  the  action  of  light  is  visible  upon  it,  it  is 
then  too  late  to  procure  a  Daguerreotype  photographic  picture. 

These  pictures  can  never  represent  the  relations  between  lights 
and  shadows  with  perfect  accuracy,  owing  to  the  different  action 
of  the  various  colors  upon  the  iodized  plate;  green  rays  scarcely 
produce  any  action,  on  which  account  trees  always  appear  very 
dark ;  red  rays,  likewise,  act  very  slightly.  Owing  to  this  cir- 
cumstance, the  Daguerreotype  portraits  do  not  produce  correct 
likenesses  of  the  originals. 

Talbot  has  pursued  a  totally  different  method  in  procuring  his 
photographic  pictures.  He  makes  use  of  a  paper  which  is  ren- 
dered peculiarly  susceptible  to  light  by  a  process  which  we  cannot 
further  describe,  and  which  is  termed  Calotype  paper.  A  negative 
picture  is  formed  upon  this  paper  in  the  Camera  Obscura,  and 
fixed  by  means  of  bromide  of  potassium. 

This  negative  picture  is  then  laid,  together  with  a  piece  of  simi- 


346  PHOTOGRAPHY. 

larly  prepared  paper,  between  two  glass  plates;  the  dark  portions 
of  the  picture  keep  from  the  second  paper  the  light  which  acts 
through  the  light  parts,  and  thus  a  positive  picture  is  formed  upon 
the  second  paper.  Several  positive  copies  may  be  taken  from  one 
and  the  same  negative  picture.* 


*  [For  full  accounts  of  the  various  kinds  of  photography,  and  the  processes 
employed,  see  "  Photogenic  Manipulation,"  by  G.  T.  Fisher,  a  useful  little  manual  on 
this  subject,  republished  by  Carey  and  Hart.] 


MAGNETISM.  347 


SECTION  VI. 

MAGNETISM    AND    ELECTRICITY 


PART  I. 

MAGNETISM. 

CHAPTER  I. 

MUTUAL  ACTION  OF  MAGNETS  ON  EACH  OTHER,  AND  ON  MAGNETIC 

BODIES. 

WE  find  in  the  bowels  of  the  earth  certain  iron  ores  which  pos- 
sess the  property  of  attracting  iron;  these  are  termed  natural 
magnets.  The  same  property  can  be  imparted  temporarily  to  iron, 
and  permanently  to  steel,  and  magnets  formed  of  this  substance, 
which  are  termed  artificial  magnets,  are  best  adapted  to  the  inves- 
tigation of  the  laws  of  magnetism,  from  the  facility  with  which 
a  suitable  form  can  be  applied  to  them.  Artificial  magnets  are 
generally  made  in  the  shape  of  rods,  needles,  or  horse-shoes. 

Magnetic  Poles. — If  we  dip  a  magnetic  rod  into  iron  filings,  we 
shall  see,  on  removing  it,  that  the  filings  will  not  be  equally  sus- 
pended to  all  parts  of  the  rod ;  they  will  fall  off  immediately  from 
the    middle,  where    the 
magnetic  rod  does  not  ap- 
pear to  exert  any  influ- 
ence ;   from   the   middle 
towards  the  extremities  or 
poles,  however,  this  power 
of  attraction  increases,  as  may  be  seen  in  Fig.  319. 

One  would  be  led,  at  first  sight,  to  suppose  that  if  a  magnet 
were  separated  along  its  neutral  line  (by  a  magnetized  steel  wire, 
for  instance,  with  which  the  experiment  may  be  easily  made), 


348  SIMILAR    POLES    REPEL    EACH    OTHER. 

neither  of  the  divided  portions  would  be  true  magnets,  and  that 
each  would  attract  at  one  extremity  only ;  experiment  proves  the 
reverse,  however,  each  part  being  a  perfect  magnet,  having  its 
neutral  line  and  two  poles. 

Similar  poles  repel  each  other,  contrary  poles  attract  each  other. — 
Fig.  320  represents  a  magnet  lying  in  a  casing  of  paper  or  metal, 
Fig>  320.  and  suspended  in  a  horizontal  posi- 

tion. If  we  bring  one  pole  of  a 
magnet  near  either  of  the  two  poles 
a  and  b  of  another  magnet,  the  pole 
a  will  be  attracted  while  b  will  be 
repelled.  We  term  the  poles  a  and 
b  opposite  poles,  because  they  act  in 
different  ways  upon  the  same  pole 
if  brought  near  them.  If,  now,  we 
invert  the  magnet  which  we  hold  in  our  hand,  in  order  to  bring 
its  opposite  pole  to  the  suspended  magnet,  the  reverse  will  take 
place,  a  will  be  repelled  and  b  attracted.  The  two  poles  of  the 
magnet  in  the  hand  are,  therefore,  also  of  different  natures,  and 
are  consequently  opposite.  In  a  similar  manner  we  may  show 
that  the  two  poles  of  every  magnet  are  opposite. 

If  we  bring  two  different  magnets  to  the  suspended  magnet,  it 
will  be  easy  to  find  which  of  the  two  attracts  the  pole  a  of  the 
suspended  magnet,  and  repels  b.  If  we  designate  this  pole  of  the 
first  magnet  as  n,  and  the  pole  of  the  second  magnet  acting  simi- 
larly as  n',  n  and  nf  will  be  the  similar  poles  of  these  two  magnets. 
If  the  second  pole  of  the  first  magnet  be  m,  and  that  of  the  other 
mr,  the  pole  m  as  well  as  m!  will  repel  the  pole  a  of  the  suspended 
magnet,  and  attract  the  pole  b.  The  two  poles  m  and  m!  are  like- 
wise similar. 

If,  now,  we  suspend  the  magnet  whose  poles  are  designated  m 
and  m!,  in  such  a  manner  as  to  admit  of  its  turning  readily  in  a 
horizontal  plane,  and  bring  the  other  near  it,  we  shall  find  that 
the  poles  m  and  m!  will  repel  each  other,  as  will  also  the  poles  n 
and  n' ;  similar  poles  consequently  repel  each  other.  While  the 
poles  m  and  n'  and  n  and  m!  being  dissimilar  poles,  attract  each 
other. 

There  are,  therefore,  in  the  two  halves  into  which  a  magnet  is 
divided  by  the  neutral  line,  two  forces,  which,  although  appearing 
at  first  sight  to  be  of  similar  nature,  from  their  acting  similarly 


INFLUENCE    OF    A   MAGNET.  349 

upon  iron  are  actually  two  opposite  forces.  The  neutral  line  is, 
consequently,  the  boundary  between  two  opposite  forces,  forming 
the  transition  from  one  to  the  other,  and  herein  lies  the  reason  of 
their  neutral  character. 

For  reasons  which  we  shall  presently  better  understand,  one 
pole  of  the  magnet  is  termed  the  south  pole,  and  the  other  the 
north  pole. 

Under  the  influence  of  a  Magnet,  iron  itself  becomes  magnetic. — 
In  order  to  show  this  property  of  iron,  we  must  make  the  experi- 
ment represented  in  Fig.  321.  Let  an  iron  cylinder  f  be  sup- 
ported by  a  magnet  a  b  ;  if  we  bring  iron  filings  to  the  lower  part 
of  this  cylinder,  they  will  continue  suspended  to  it  in  the  form  of 
a  little  tuft  hanging  as  long  as  the  little  cylinder 
continues  to  adhere  to  the  magnet ;  but,  as  soon 
as  the  cylinder  is  removed,  the  iron  filings  will 
fall  off,  and  no  further  attractive  force  be  per- 
ceived. We  cannot  ascribe  this  phenomenon  to 
the  force  of  the  magnet  acting  at  a  distance,  for,  if  the  small 
cylinder  were  not  of  iron,  we  should  not  observe  the  phenomenon  ; 
of  this  we  shall  be  still  better  convinced  by  observing,  1,  that  the 
threads  of  iron  filings  diminish  gradually  from  the  extremity  of  the 
cylinder ;  2,  that  there  is  a  point  towards  the  upper  end  where  the 
filings  do  not  adhere,  consequently,  that  the  small  cylinder  has  a 
neutral  magnetic  line ;  3,  that  the  filings  adhere  again  above  this 
point,  but  that  they  have  an  opposite  direction.  The  little  cylin- 
der is,  therefore,  a  real  magnet,  attracting  iron  filings,  having  two 
poles,  and  a  neutral  magnetic  line;  the  latter,  however,  does  not 
coincide  with  the  geometrical  middle. 

Instead  of  bringing  iron  filings  to  the  suspended  cylinder,  we 
may  attach  to  it  another  cylinder  (as  in  Fig.  Fig  322> 

322)  which  will  also  be  supported  ;  to  this  a 
third,  fourth,  and  so  on ;  in  this  way  a  chain 
may  be  formed,  of  which  the  magnet  is  the 
first  link.  If  we  remove  this  link,  the  whole 
:hain  will  fall  apart,  there  being  no  power  to  hold  the  links  to- 
gether. 

Magnetic  Fluids.— To  explain  the  various  phenomena  of  mag- 
letism,  we  assume  that  there  are  two  different  magnetic  fluids, 
listributed  in  the  magnet  in  a  manner  which  we  must  consider 
nore  particularly;  the  particles  of  both  of  these  fluids  repel  each 


350  MAGNETIC    FLUIDS. 

other,  but  attract  those  of  the  other  fluid.  The  magnetic  fluids 
are  present  in  equal  quantities  in  every  molecule  of  iron  and  steel; 
but  they  cannot  pass  from  a  magnet  to  a  piece  of  iron,  or  from  one 
molecule  to  another,  the  magnetic  condition  depending  only  upon 
the  manner  in  which  the  magnetic  fluids  are  distributed  in  every 
individual  molecule. 

We  must  suppose  a  magnet,  or  a  magnetized  iron  rod  (as  seen 
in  Fig.  323)  to  be  composed  of  small  particles,  each  of  which 
contains  both  fluids,  although  in  a  state  of  separation ;  the  mag- 
netic fluids  being  distributed  in  each  particle  in  such  a  manner 
Fi    323  that   the    similar   fluid    is 

turned  towards  the  same 
side  in  all  the  particles. 
There  is,  therefore,  only  one 
fluid  present  at  the  left  ex- 
tremity of  the  magnet  represented  in  Fig.  323,  while  the  right 
extremity  is  solely  occupied  by  the  other ;  the  polarity  of  the 
magnet  is  thus  explained.  We  can  easily  understand  from  this 
explanation  that  a  magnet  may  be  broken  into  two  parts,  and 
each  separate  portion  remain  a  perfect  magnet. 

If,  therefore,  a  piece  of  iron  be  magnetized  by  the  influence  of 
a  magnet,  no  magnetic  fluid  will  pass  from  the  magnet  to  the  iron, 
but  the  approximation  of  the  magnet  will  simply  occasion  a  dis- 
tribution through  the  iron  of  the  magnetic  fluids  which  have  not 
hitherto  been  separated  in  each  molecule,  and  directed  towards  a 
definite  side,  but  distributed  quite  uniformly  over  the  whole. 

Iron  only  retains  its  magnetic  properties  so  long  as  the  con- 
tiguity of  a  magnet  keeps  the  magnetic  fluids  separated ;  on  the 
removal  of  the  magnet  the  separated  fluids  again  combine,  and  the 
iron  returns  to  its  natural  condition. 

A  horizontal  magnet  a  b  supports  at  one  end  an  iron  massy,  the  I 
weight  of  which  is  nearly  as  great  as  the  magnet 
is  capable  of  supporting.     We  now  bring  another  . 
magnet  af  br  over  a  b  in  such  a  manner  that  the 
contrary  poles  a  and  b'  are  turned  towards  each 
other.     If  we  bring  the  second  magnet  gradually 
nearer,  in  the  manner  specified,  the  piece  of  iron  i 
f  will  fall  off.    The  two  magnets  combined  cannot  •  j 
therefore,  support  as  much  as  each  one  separately.  We  may  easily 
understand  the  cause  of  this;  for  the  second  magnet  disturbs  the[ 


MAGNETIC    ARMATURES.  351 

actions  of  the  first,  whilst  it  decomposes  the  fluids  of  the  mass  of 
iron  f  in  an  opposite  sense. 

Steel  resists  the  magnetizing  influence  of  a  magnet  much  better 
than  iron,  that  is  to  say,  a  piece  of  steel,  if  it  be  tolerably  large,  is 
not  magnetized  so  strongly  or  immediately  by  contact  with  a  mag- 
net as  is  a  piece  of  iron  ;  and  in  order  perfectly  to  magnetize  a  rod 
of  steel,  it  is  necessary  that  it  should  be  for  a  longer  period  in  con- 
tact with  the  magnet,  or  that  the  latter  should  be  drawn  repeat- 
edly over  it  in  the  proper  manner  ;  when,  however,  steel  is  once 
magnetized,  it  does  not  lose  this  property  very  easily,  but  retains 
the  magnetic  character  even  after  the  magnet  has  been  removed; 
we  may,  consequently,  form  permanent  magnets  of  steel,  but  not 
of  iron. 

Perfectly  hardened  steel  admits  least  easily  of  being  mag- 
netized ;  but  when  once  it  has  acquired  the  magnetic  property,  it 
does  not  readily  lose  it.  When  tempered  steel  loses  its  hardness 
by  being  annealed,  it  assimilates  more  nearly  to  soft  iron  in  its 
relation  to  magnetism.  Red  hot  iron  is  not  attracted  by  a  mag- 
net, and  a  steel  magnet  entirely  loses  its  magnetic  properties  on 
being  heated. 

Besides  iron,  nickel  and  cobalt  may  also  become  magnetic. 

Magnetic  Jlrmatures. — A  magnet  may  gradually  lose  its  force, 
owing  to  various  causes.     To  prevent  this,  the  so  called  arma- 
tures are  made  use  of:  this  term  is  applied  to  pieces  of  soft  iron, 
brought  into  contact  with  the  magnet  in  order  to  preserve  its 
power  by  means  of  the  magnetic  decomposition  going  on  in  the 
soft  iron.     The  following  method,  for  thus  arming  magnetic  bars, 
|  is  the  best,  and  will  be  seen  exemplified  in  Fig.  325.     Two  like 
magnetic  bars  are  laid  parallel  to  each  other,  in  such 
a  manner  that  the  north  pole  of  the  one  is  directed  to 
the  same  side  as  the  south  pole  of  the  other,  to  these 
are  attached  two  pieces  of  soft  iron ;  a  b  and  c  dy  in 
order  to  complete  the  parallelogram.     Each  of  these 
pieces  of  iron  naturally  becomes  a  magnet  of  itself, 
reacting  in  such  a  manner  upon  the  magnetic  rods 
JV  S  and  Nf  Sf,  that  the  separated  fluids  are  fixed  at 
the  corresponding  extremities. 

Magnetic  needles,  and  bars  lying  in  the  direction  of  terrestrial 
magnetism,  may  be  considered  as  in  some  degree,  armed  by  the 
earth. 


352 


COULOMB'S    PLAN. 


A  magnetic  battery  is  a  combination  of  several  individual 
magnets.     Fig.   326   represents   one    constructed   according  to 

Fig.  326. 


Coulomb's  plan.  It  consists  of  12  separate  magnetic  bars,  form- 
ing 3  layers  each,  composed  of  4  bars.  The  bars  of  the  middle 
layer  are  about  2,  5,  or  3  inches  shorter  than  those  of  the  other 
layers,  and  project  about  15  to  18  lines  at  either  side.  All  the 
bars  are  of  exactly  the  same  thickness,  and  are  fastened  into 
pieces  of  irony  serving  as  armatures.  The  brass  bands  c  d  serve 
to  hold  the  rods  and  armatures  together.  Such  large  magnetic 
bundles  remain  horizontally  fixed,  when  made  use  of  for  the  pur- 
pose of  magnetizing.  The  smaller  ones,  employed  for  friction, 
are  constructed  on  similar  principles. 

Fig.  327  represents  a  horse-shoe  magnet.  It  consists  of  several 
horse-shoe  shaped  curved  plates  of  steel,  lying  immediately  on 
one  another,  and  held  together  by  two  screws  a  and  a,  made  of 
iron  or  brass.  Each  plate  is  separately  magnetized,  before  it  is 
used  for  constructing  the  apparatus.  A  ring  n  n'  serves  to  sus- 
pend the  magnets,  and  a  piece  of  soft  iron  p  pf,  the  anchor,  forms 
the  armature.  Good  horse-shoe  magnets  are  capable  of  sustaining 
from  10  to  20  times  their  own  weight. 


Fig.  327. 


Fig.  328. 


Fig.  329. 


MAGNETIZATION  OF  STEEL  NEEDLES  AND  BARS.   353 

The  armature  of  natural  magnets  is  represented  in  Figs.  328 
and  329.  The  parts  /  and  V  are  the  wings  of  the  armature,  and 
p  p'  the  feet.  The  wings  are  made  nearly  as  broad  as  the  mag- 
net, and  about  one  line  in  thickness.  The  dimensions  of  the  feet 
depend  upon  the  strength  of  the  magnets. 

A  remarkable  phenomenon  is  observed  in  natural  as  well  as 
artificial  magnets,  which  has  not  as  yet  been  satisfactorily  ex- 
plained, we  mean  the  weakening  which  occurs  on  overloading. 
Let  us  assume  that  a  magnet  can  bear  40  pounds.  If,  now,  we 
daily  add  a  small  weight,  we  increase  its  power  of  bearing  until 
the  load  amount  to  60  or  80  pounds ;  as  soon,  however,  as  the 
lifter  is  severed  by  the  application  of  too  large  a  weight,  the 
strength  of  the  magnet  diminishes  considerably,  scarcely,  at  last, 
supporting  more  than  40  pounds,  the  weight  from  which  we 
started.  But  if  we  attach  a  smaller  weight,  increasing  it  with 
caution,  we  shall  find  that,  after  some  time,  the  magnet  has 
recovered  its  former  strength. 

Magnetization  of  Steel  Needles  and  Bars.— The  so-called  method 
by  separated  touch,  is  managed  by  placing  two  strong  bundles  of 
magnets,  see  Fig.  326,  in  such  a  manner  that  the  axis  of  the  one 
coincides  with  the  line  of  prolongation  of  the  axis  of  the  other,  and 
that  the  opposite  poles  are  inclined  towards  each  other,  as  seen  in 
Fig.  330,  where  f  represents  the  one  pole  of  one  bundle,  and 

!/'  the   opposite  pole  of  Fjg  330> 

i  the  other.     The  needle 

|  to  be  magnetized  is  now 
laid  upon  a  piece  of  wood 
/,  to  which  it  may  be  se- 
cured to  prevent  its  be- 
ing displaced.  We  now  take  the  two  touching  magnets  g  and  g*, 
each  in  one  hand,  and  holding  them  at  an  inclination  of  about 
25  or  30  degrees  towards  the  horizon,  place  them  in  the  middle 
of  the  rod  to  be  magnetized,  moving  them  gently  and  regularly 
in  such  a  manner  that  g  g'  simultaneously  reach  the  opposite 
extremities  of  the  needle,  and  this  process  is  repeated  several 

!  times.     It  will,  of  course,  be  understood  that  the  touching  magnet 
must  touch  the  needle  with  the  same  pole  towards  which  we  direct 

|  it.    This  method  is  especially  well  adapted  to  magnetize  regularly 

'and  perfectly  such  magnets  as  are  used  for  compasses,  or  steel 
bars  which  are  not  more  than  1  or  2  lines  in  thickness. 

30* 


354  DIRECTION   OF   MAGNETS. 

The  double  touch  is  applied  to  prepare  steel  bars  which  exceed 
1  or  2  lines  in  thickness ;  in  which  case,  the  method  above  de- 
scribed is  inadequate  to  the  purpose.  The  double  touch  is  thus 

managed.  The  bar  to 
be  magnetized  is  laid 
between  two  bundles 
of  magnets,  which  are 
placed  over  its  centre 
as  described  in  the  for- 
mer method;  the  magnets  must,  however,  be  less  inclined, form- 
ing only  an  angle  of  from  15  to  20  degrees  with  the  horizon. 
Besides  this,  the  frictions  are  not  made  towards  opposite  poles, 
but  both  magnets  are  moved  towards  one  extremity  of  the  rod, 
and  then  back  the  whole  length.  After  the  magnets  have  been 
moved  together  sufficiently  long,  they  are  again  raised  from  the 
middle  of  the  rod.  In  order  to  manage  this  process  more  conve- 
niently, we  may  fasten  the  two  rubbing  magnets  to  a  kind  of  tri- 
angle of  wood  or  brass ;  there  must,  however,  at  all  events,  be  a 
space  of  about  2  or  3  lines  between  the  lower  parts  of  the  mag- 
nets ;  this  is  best  effected  by  the  insertion  of  a  bit  of  wood,  brass, 
or  lead,  as  represented  in  our  Fig.  at  /. 

The  double  touch  communicates  a  very  strong  degree  of  mag- 
netism, but  it  cannot  be  safely  applied  to  magnetize  needles  for 
compasses,  or  bars  intended  for  nice  experiments,  since  it  almost 
always  gives  poles  of  unequal  strength,  thus  occasioning  succes- 
sive stoppages. 


CHAPTER    II. 

OF  THE  MAGNETIC  ACTIONS  OF  THE  EARTH. 

Direction  of  Magnets,  Declination,  Inclination.  —  A  mag- 
netic rod,  horizontally  suspended  by  a  silk  thread,  or  a  magnetic 
needle,  revolving  easily  upon  a  point  in  a  horizontal  plane,  (this 
needle  is  generally  made  in  the  form  of  a  rhomboid,  as  seen  in 
Fig.  332,  and  has  in  its  centre  an  agate  cap,  which  reposes  upon 
the  steel  point  forming  the  pivot,)  is  not  in  equilibrium  in  all  po- 


DECLINATION— INCLINATION. 


355 


Fig.  332. 


sitions,  but  takes  a  definite  position,  directed  towards  one  definite 
point  of  the  horizon.  It  will  always  return  to  this  position  after  a 
series  of  oscillations,  if  removed 
from  it.  The  force  urging  the 
needle  back  to  this  position  is 
magnetic;  since  no  phenomenon 
of  the  kind  is  exhibited  in  the  case 
of  an  unmagnetized  needle.  This 
remarkable  property  of  magnetism 
is  observed  everywhere;  in  all 
parts  of  the  world,  on  all  seas,  on 
the  loftiest  summits  of  mountains, 
as  in  the  deepest  mines,  the  mag- 
netic needle  assumes  a  definite 

direction,  to  which  it  will  inva-  ^^ 

riably  return  if  removed  from  it. 

There  must,  consequently,  be  a  magnetic  force  which  acts  at  all 
points  of  the  earth's  surface,  for  magnetic  needles  can  no  more 
take  up  a  direction  of  themselves,  than  a  body  can  set  itself  into 
motion ;  in  both  cases  the  influence  of  some  foreign  force  is  re- 
quired. We  may  prove,  by  means  of  a  simple  experiment,  that 
this  directing  force  acts  as  a  magnet,  and  not  as  a  mass  of  iron. 
If  we  entirely  invert  the  poles  of  a  magnetic  needle,  they  will  not 
be  in  equilibrium  in  their  new  position,  but  will  each  describe 
a  complete  semicircle  in  order  to  return  to  the  state  of  equilibrium, 
and  reassume  their  original  direction.  The  directing  force,  con- 
sequently, distinguishes  the  two  poles,  attracting  the  one,  and  re- 
pelling the  other  like  a  magnet,  whilst  iron  will  equally  attract 
the  poles  of  a  magnet. 

When  we  combine  all  the  different  observations  that  have  been 
made  in  different  places,  we  are,  in  truth,  led  to  regard  the  earth 
as  one  great  magnet,  whose  neutral  line  is  situated  in  the  region 
of  the  equator.  Hence  we  have  a  means  offered  us  of  giving 
fitting  terms  to  the  two  poles  of  a  magnet. 

The  two  poles  of  the  great  terrestrial  magnet  lie  in  the  vicinity 
of  the  poles  of  the  earth's  axis,  on  which  account  we  name  the 
one  the  magnetic  north  pole,  and  the  other  the  magnetic  south  pole. 
These  contrary  poles  attract  each  other,  however,  and  thus  a  mag- 
netic needle  will  turn  its  south  pole  to  the  north,  and  its  north 
pole  to  the  south. 


356 


THE    MAGNETIC    MERIDIAN. 


This  designation  is  not,  however,  universally  received,  since 
some  designate  the  poles  of  a  magnetic  needle  in  a  totally  oppo- 
site manner,  giving  the  name  of  north  pole  to  that  pole  which 
turns  towards  the  north. 

If  we  suspend  two  magnetic  needles  at  the  same  place  at  such 
a  distance  that  they  exert  no  influence  on  each  other,  each  will 
assume  a  direction  parallel  with  that  of  the  other.  This  paral- 
lelism does  not,  however,  prevail  for  places  separated  by  the  dis- 
tance of  several  degrees  of  latitude  or  longitude  from  each  other. 
It  is  of  the  greatest  importance  to  be  able  to  determine  the  direc- 
tion of  magnetic  needles,  that  is,  to  compare  them  with  lines  of 
unvarying  position,  in  order  to  ascertain  the  variations,  occurring 
in  the  course  of  time,  at  one  and  the  same  place  in  the  direction 
of  the  magnetic  needle,  and  the  relations  existing  between  the 
direction  of  magnetic  needles  at  different  places. 

The  Magnetic  Meridian  is  the  vertical  plane,  we  may  suppose, 
passing  through  the  line  of  direction  of  a  horizontal  magnet,  or 
simply  the  section  of  this  plane  with  the  earth's  surface.  The 
magnetic  meridian  of  a  place  makes  with  the  astronomical  meri- 
dian an  angle,  termed  the  declination  or  deviation.  The  declina- 
tion is  east  or  west,  according  as  the  magnetic  needle  deviates 
towards  one  or  the  other  side  of  the  astronomical  meridian.  In 
Fig.  333,  for  instance,  s  n  represents  the  meridian  of  a  place,  and 
a  b  the  direction  of  the  horizontal  magnetic  needle  at  the  same 
place.  The  western  declination  amounted  to  18°  37'  30,55"  at 
Gottingen  in  January,  1837.  We  shall  presently  see  that  the  de- 
clination varies  with  the  time.  There  are  places  on  the  earth 
where  the  direction  of  the  magnetic  needle  exactly  coincides  with 


Fig.  333. 


Fig.  334. 


THE   MAGNETIC    MERIDIAN.  357 

the  meridian.     At  these  places  the  declination  is,  of  course,  null, 

at  0. 
very  apparatus  serving  to  measure  declination  is  termed  a 

lination  compass. 

ig.  334  represents  a  compass  of  simple  construction.  The 
.t  to  which  the  needle  is  suspended  is  the  centre  of  a  gradu- 
ated horizontal  circle,  which  may  revolve  about  a  vertical  axis  in 
its  own  plane.  To  the  side  of  the  box  a  telescope  is  attached, 
whose  axis  runs  parallel  with  the  line  which  we  may  suppose 
drawn  from  0  on  the  graduated  circle,  through  its  central  point,  to 
the  line  marked  180°.  On  revolving  the  horizontal  circle  in  its 
plane,  the  extremity  of  the  magnetic  needle  points  towards  other 
lines  of  the  circle.  If  we  place  the  apparatus  in  such  a  manner 
as  to  let  the  needle  point  to  0  of  the  scale,  the  axis  of  the  tele- 
scope will  be  parallel  with  the  needle,  coinciding  with  the  mag- 
netic meridian ;  but  in  every  other  position  the  needle  will  point 
to  that  number  of  the  circle  marking  the  number  of  degrees  of 
which  the  angle  consists,  which  the  direction  of  the  needle  makes 
with  the  axis  of  the  telescope ;  if,  therefore,  we  bring  the  telescope 
exactly  into  the  astronomical  meridian,  we  shall  see  on  the  gradu- 
ated circle  the  angle  made  by  the  magnetic  with  the  astronomical 
meridian. 

This  instrument  serves  especially  for  the  measurement  of 
angles,  since  we  can,  at  all  times,  make  use  of  it  to  determine 
the  angle  which  the  optical  axis  of  the  telescope  (or  rather  its 

izontal  position)  makes  with  the  magnetic  meridian. 

The  declination  compass,  generally  used  at  sea,  is  known  by 

e  name  of  the  Mariner's  Compass. 

On  the  whole,  the  direction  of  the  magnetic  needle  inclines 
more  to  the  north  and  south  than  to  the  east  and  west;  hence,  it 
is  usual  to  say,  that  the  magnetic  needle  points  to  the  north. 

The  magnetic  needles  we  have  been  considering,  are  suspended 
in  such  a  manner  as  only  to  revolve  in  a  horizontal  plane,  that  is, 
about  a  vertical  axis.  In  the  mode  of  suspension,  represented 
in  Fig.  320,  and  also  in  Fig.  332,  the  horizontal  position  is  main- 
tained by  the  centre  of  gravity  of  the  needle  being  below  the  point 
of  suspension.  As  soon,  however,  as  we  suspend  a  magnetic 
needle  in  its  centre  of  gravity,  it  will  not  remain  equipoised,  but 
will  make,  with  the  horizon,  an  angle,  which  is  termed  the  inclina- 
tion. 

The  apparatus,  represented  in  Fig.  335,  is  well  adapted  to 


358 


THE    MAGNETIC    MERIDIAN. 


show  the  inclination  of  the  magnetic  needle.     In  a  brass  frame, 
suspended  by  a  thread,  there  is  a  horizontal  axis  a  b  which  moves 


Fig.  335. 


Fig.  336. 


very  readily,  passing  through  the  centre  of  gravity  of  the  magnetic 
needle.  We  see  that  a  magnetic  needle,  thus  suspended,  can 
easily  move  round  a  vertical  or  a  horizontal  axis,  and,  therefore, 
that  it  can  freely  follow  the  directing  influence  of  the  earth.  The 
needle  places  itself  in  such  a  position,  that  its  line  of  direction 
coincides  with  the  magnetic  meridian ;  but  the  extremity  of  the 
needle,  turned  towards  the  north,  dips;  consequently,  the  line  of 
direction  of  the  needle,  makes  an  angle  with  the  horizon,  which, 
in  our  part  of  the  world,  amounts  to  about  70°. 

If  the  needle  of  inclination  be  applied  to  a  graduated  vertical 
circle,  whose  planes  coincide  with  the  plane  of  rotation  of  the 
needle,  as  seen  in  Fig.  336,  we  may  ascertain  the  amount  of 
inclination  on  this  circle,  by  making  the  plane  of  the  vertical 
circle  coincide  exactly  with  the  magnetic  meridian. 

An  apparatus  serving  to  measure  the  amount  of  inclination,  is 
termed  a  dipping  needle,  or  a  compass  of  inclination. 

The  inclination  generally  increases  as  we  approach  nearer  to 
the  north ;  in  many  places  the  dipping  needle  assumes  an  almost 
vertical  position;  thus,  for  instance,  in  the  year  1773,  Captain 
Phipps  observed,  at  79°  44'  north  latitude,  an  inclination  of  82°  9', 
and  Parry,  an  inclination  of  88°  43',  in  latitude  70°  47'.  Captain 


THE    MAGNETIC    MERIDIAN.  359 

Ross  has,  at  last,  reached  the  magnetic  north  pole  of  the  earth. 
At  70°  5'  N.  lat.,  and  263°  14'  E.  long.,  from  Greenwich,  he 
found  the  inclination,  or  dip,  to  be  90°.  The  inclination  of  the 
magnetic  needle  is  so  considerable  in  high  latitudes,  that  the 
compass  loses  much  of  its  practical  utility,  as  has  been  shown  in 
the  late  North  Polar  Expedition. 

The  further  we  advance  towards  the  south,  the  more  the  incli- 
nation decreases,  and  at  the  equator  we  come  to  a  point  where  it 
is  absolutely  null,  where,  consequently,  the  needle  of  inclination 
is  perfectly  horizontal ;  as  we  advance  further  to  the  south,  we 
again  observe  an  inclination,  but  it  is  in  an  opposite  direction, 
the  extremity  of  the  needle  pointing  to  the  south  being  the  one 
that  now  dips.  This  inclination  increases  likewise  with  the 
increase  of  southern  latitude.  In  the  vicinity  of  the  south  pole  of 
the  earth,  there  is,  therefore,  a  second  point  at  which  the  dipping 
needle  stands  perfectly  vertical,  and  this  is  the  south  magnetic 
pole. 

At  whatever  degree  of  geographical  longitude  we  may  pass  this 
equatorial  zone,  we  shall  always  find  one  point  where  the  needle 
will  be  perfectly  horizontal.  These  places  where  there  is  no 
inclination  form  a  curve  all  round  the  earth,  termed  the  magnetic 
equator. 

The  magnetic  equator  does  not  coincide  with  the  terrestrial 
equator,  or  form  any  regular  circle  of  the  earth's  sphere.  It 
attains  its  greatest  southern  latitude  on  the  Atlantic  Ocean  at 
about  28°  W.  of  Paris,  (25°  40'  W.  of  Greenwich,)  where  it  is  then 
about  14°  degrees  south  of  the  terrestrial  equator.  The  two 
equators  approach  each  other  as  they  incline  to  the  west,  meeting 
at  120°  W.  of  Paris  (117°  40'  W.  of  G.);  here,  however,  instead 
of  turning  to  the  northern  hemisphere,  it  again  inclines  to  the 
south  about  160°  W.  of  Paris  (157°  40'  W.  of  G.),  in  order  to  reach 
a  second  southern  maximum  of  3°  75'.  At  174°  long,  it  cuts  the 
terrestrial  equator,  and  remaining  within  the  northern  hemisphere, 
intersects  the  terrestrial  equator  again  at  18°  E.  of  Paris  (20°  20' 
E.  of  G.).  The  magnetic  equator  has  a  N.  lat.  of  11°  47'  at  62° 
E.  of  Paris  (64°  20'  E.  of  G.);  while  it  is  7°  44'  at  150°  E.  of 
Paris  (152°  20'  E.  of  G.),  and  8°  57'  at  130°  E.  of  Paris  (132°  20' 
E.  of  G.).  These  data  will  suffice  to  define,  in  general  terms,  the 
position  of  the  magnetic  equator,  and  the  irregularity  of  its  course. 

The  total  action  exerted  by  the  earth  upon  a  magnetic  needle, 


360       VARIATIONS    OF    DECLINATION    AND    INCLINATION. 

is  simply  directive ,  not  attractive,  since,  if  it  were  the  latter,  a 
magnetic  needle  would  necessarily  weigh  more  than  before  it 
was  magnetized.  If  we  lay  a  magnetic  needle  upon  a  cork  swim- 
ming in  water,  it  will  move  into  the  magnetic  meridian,  without 
evincing  any  tendency  to  float  towards  the  north,  as  we  might 
expect. 

If  we  bring  a  magnet  near  a  floating  needle,  either  attraction 
or  repulsion  will  occur,  according  to  the  pole  of  the  magnet 
nearest  it ;  the  needle  either  approaching  to,  or  receding  from 
the  magnet.  Why  does  not  the  needle  move  towards  the  north 
magnetic  pole,  if  the  earth  be  nothing  more  than  a  large  magnet? 
The  reason  is  this:  the  force  of  magnetic  attraction  diminishes 
with  the  distance,  as  we  shall  soon  see.  If  we  direct  a  magnet 
towards  the  floating  needle,  the  two  poles  of  the  needle  will  not 
be  equally  distant  from  the  pole  of  the  magnet ;  consequently  the 
repulsive  or  the  attractive  force  must  preponderate,  and  forward 
motion  be  produced.  The  north  magnetic  pole  of  the  earth  is, 
however,  so  extremely  remote  from  the  floating  needle,  that  the 
length  of  the  needle  does  not  bear  any  appreciable  proportion  to 
the  distance ;  the  one  pole  of  the  needle  is,  therefore,  as  much 
attracted  as  the  other  is  repulsed. 

Variations  of  Declination  and  Inclination. — The  declination, 
like  the  inclination,  is  variable  ;  thus,  in  the  year  1580,  the  decli- 
nation at  Paris  was  11°  30'  E.,  it  then  diminished,  and  was  null 
in  the  year  1663;  from  this  time  the  declination  inclined  to  the 
westward,  increasing  constantly  till  the  year  1814,  when  it 
attained  its  maximum  west,  amounting  to  22°  34',  and  again 
began  to  decrease. 

The  inclination  of  the  magnetic  needle  at  Paris  has  constantly 
diminished  from  the  year  1671,  when  it  amounted  to  about  75°, 
it  being  now  about  67J°  [The  declination  in  London  was  11°  16' 
in  1580,  and  was  null  in  1660,  and  then  inclining  to  the  west- 
ward, gradually  increased  in  that  direction  until  1818,  when  it 
attained  24°  30'  since  which  it  has  decreased. 

The  inclination  of  the  needle  at  London  was  74°  30'  in  1680, 
since  which  it  has  gradually  lessened  to  about  67°.] 

These  gradual  changes  of  declination  and  inclination  are  called 
secular  variations;  they  are  not,  however,  the  only  changes  to 
which  the  direction  of  the  declination  is  subject. 

If  we  carefully  observe  the  declination  needle,  we  shall  find 


INTENSITY    OF    TERRESTRIAL   MAGNETISM.  361 

that  it  continually  makes  small  oscillations,  moving  alternately 
from  east  to  west  from  its  position  of  equilibrium ;  these  oscilla- 
tions are  sometimes  regular  and  periodical,  sometimes  accidental 
and  abrupt.  The  former  are  termed  the  diurnal  variations,  the 
latter  perturbations.  In  general,  the  north  end  of  the  needle 
continues  its  onward  motion  westward  from  sunrise,  and  begins 
its  retrograde  motion  about  5  P.M. 

The  amplitude  of  the  diurnal  variations,  that  is,  the  angle  be- 
tween the  eastern  and  western  limits,  varies ;  being  sometimes 
only  5  or  6  seconds,  and  sometimes  amounting  to  J  minute. 

The  inclination  is  likewise  subject  to  similar  variations. 

The  needle  of  declination  makes  very  strong  irregular  oscilla- 
tions, amounting  often  to  more  than  a  degree,  on  the  appearance 
of  an  aurora  borealis  in  the  heavens. 

Earthquakes  and  volcanic  eruptions  also  appear  to  act  upon  the 
magnetic  needle,  producing  frequently  a  permanent  change  in  its 
position. 

Intensity  of  Terrestrial  Magnetism.— If  a  needle  of  inclination 
be  drawn  out  of  the  magnetic  meridian,  terrestrial  magnetism  will 
endeavor  to  restore  it  to  its  position  of  equilibrium  ;  it  is  only  on 
leaving  the  needle  entirely  to  itself,  that  it  will,  after  a  series  of 
vibrations,  resume  its  position  of  rest.  The  period  necessary  for 
each  one  of  these  vibrations  depends  upon  the  mass  of  the  needle, 
the  strength  of  the  magnetism  developed,  and  likewise  the  force  of 
terrestrial  magnetism.  Thus,  the  same  needle  will  vibrate  with 
more  or  less  rapidity,  according  to  the  force  of  the  terrestrial  mag- 
netism acting  upon  it. 

We  have  thus  a  method  of  comparing  the  force  of  terrestrial 
magnetism,  as  manifested  at  different  pi  aces  on  the  earth;  it  being 
only  necessary  to  observe  the  number  of  oscillations  made  in  a 
definite  time  (as  5  minutes  for  instance),  in  different  parts  of  the 
earth  by  the  same  needle  of  inclination,  and  by  this  mode  of 
observation  we  may  easily  reckon  how  the  force  of  terrestrial 
magnetism  stands  at  one  place  with  regard  to  that  exhibited  at 
another,  for  the  intensities  of  terrestrial  magnetism  are  as  the 
squares  of  the  number  of  oscillations  made  in  an  equal  period  of 
time. 

The  observations  made  on  the  oscillations  of  a  needle  of  incli- 
nation can  never  yield  very  accurate  results,  and,  therefore,  the 
experiments  made  on  the  oscillation  of  horizontal  needles  or  rods 
31 


362    INFLUENCE    OF    TERRESTRIAL    MAGNETISM    UPON    IRON. 

are  preferable.  The  force  causing  the  needle  of  declination  to 
vibrate,  is  only  a  portion  of  a  horizontal  lateral  force,  itself  but  a 
part  of  the  magnetic  terrestrial  force  acting  in  the  direction  of  the 
needle  of  inclination;  if,  however,  the  horizontal  intensity  and  the 
amount  of  the  inclination  be  known,  we  may  easily  compute  the 
whole  intensity. 

When  the  horizontal  intensity  of  the  terrestrial  magnetism  and 
of  the  inclination  is  known,  we  may  easily  find  the  whole  intensity 
by  construction. 

In  Fig.  337,  a  b  is  the  horizontal  intensity.     If  now  we  make 

the  angle  i  equal  to  the  inclination  observed  at  the 

Fig.  337.      same  place,  and  draw  a  perpendicular  from  6,  a  c 

a 6    will  represent  the  whole  intensity. 

If  I  =  o,  the  direction  of  the  terrestrial  magnetic 
force  will  be  in  a  horizontal  plane ;  this,  as  is  well 
known,  is  the  case  at   the   magnetic   equator,  the 
horizontal  intensity  being  here  equal  to  the  whole 
intensity.     The  horizontal  portion  of  the  magnetic 
terrestrial  force  becomes  larger,  the  nearer  we  ap- 
proach the  magnetic  equator ;  at  the  magnetic  poles  of  the  earth, 
where  the  needle  of  inclination  stands  in  a  vertical  position,  the 
horizontal  portion  of  the  terrestrial  magnetic  force  is  null. 

On  comparing  the  results  of  the  observations  that  have  been 
made  on  the  amount  of  intensity  at  different  places  on  the  earth's 
surface,  we  arrive  at  the  following  general  result,  that  the  total 
intensity  is  smallest  in  the  vicinity  of  the  magnetic  equator, 
increasing  the  further  we  move  away  from  it  towards  the  north 
or  south.  In  the  vicinity  of  the  magnetic  poles  it  is  about  1,5 
times  greater  than  at  the  equator.  The  intensity  varies  also  at 
the  same  place,  and,  like  the  declination  and  the  inclination,  is 
subject  to  diurnal  variations. 

Influence  of  Terrestrial  Magnetism  upon  Iron. — If  we  hold  a  rod 
of  soft  iron,  from  20  to  30  inches  in  length,  in  the  direction  of 
the  dip,  it  will  become  magnetic  by  the  influence  of  terrestrial 
magnetism,  its  lower  end  becoming  a  south  pole,  and  its  upper 
end  a  north  pole,  as  may  be  easily  seen  by  bringing  a  small  sen- 
sitive magnetic  needle  successively  in  the  vicinity  of  the  ends  of 
the  rod.  The  same  pole  of  the  needle  is  attracted  by  the  one  end 
of  the  rod,  and  repelled  by  the  other;  by  which  circumstance  we 
may  at  once  perceive  the  polar  magnetic  condition  of  the  rod. 


INFLUENCE    OF    TERRESTRIAL   MAGNETISM    UPON    IRON.    363 

On  inverting  the  rod  we  find  its  poles  have  changed,  the  lower 
end  being  again  a  south  pole,  and  the  upper  one  a  north  pole. 

The  same,  although  somewhat  modified  action  is  also  produced 
by  terrestrial  magnetism  on  a  vertically  suspended  iron  rod,  or, 
indeed,  on  any  iron  rod,  let  the  angle  it  makes  with  the  direction 
of  the  needle  of  inclination  be  what  it  may;  the  action  being, 
however,  less  in  proportion  as  it  recedes  from  the  direction  of  the 
needle  of  inclination.  Terrestrial  magnetism  exercises  more  or 
less  strongly  the  same  influence  on  all  masses  of  iron ;  all  soft  iron 
must,  therefore,  assume  a  polar  magnetism  under  its  influence,  as 
may  be  shown  with  more  or  less  distinctness,  according  to  cir- 
cumstances. If  a  rod  of  iron  be  magnetized  by  the  influence  of 
terrestrial  magnetism,  a  few  strokes  of  the  hammer  will  suffice  to 
fix  the  magnetism,  and,  therefore,  to  convert  the  rod  into  a  perma- 
nent magnet;  by  striking  the  iron,  a  coercive  force  is  consequently 
imparted  to  it,  which  hinders  the  union  of  those  fluids  that  have 
separated  in  the  iron  by  the  influence  of  the  earth.  We  may  thus 
understand  how  almost  all  tools  in  the  workshop  of  a  locksmith 
become  magnets.  It  appears  that  chemical  changes  act  similarly 
to  mechanical  disturbances  in  fixing  the  magnetism  imparted  by 
the  earth  to  the  iron,  for  we  find  that  iron  rods,  after  being  for 
any  length  of  time  in  a  vertical  position,  and  becoming  rusted, 
acquire  a  permanent  magnetism.  A  certain  individual,  named 
Julius  Caesar,  a  surgeon  at  Rimini,  first  observed  in  the  year  1590 
that  an  iron  rod  on  the  tower  of  the  Church  of  St.  Augustin  had 
become  magnetic  from  the  influence  of  the  earth.  At  a  subsequent 
period,  in  the  year  1630,  Gassendi  made  a  similar  observation 
with  regard  to  the  cross  on  the  steeple  of  the  Church  of  St.  John, 
at  Aix,  which  had  been  struck  down  by  lightning.  It  was  strongly 
rusted,  and  had  all  the  properties  of  a  magnet.  Since  that  time 
numerous  observations  of  this  kind  have  been  made,  and  it  has 
been  generally  found  that  iron  which  is  somewhat  rusted,  is 
always  more  or  less  magnetic. 

On  dipping  a  horse-shoe  magnet  into  iron  filings,  the  latter  will 
arrange  themselves  in  a  tuft  between  the  poles ;  if  we  then  moisten 
them  with  oil,  and  expose  them  to  a  red  heat  while  they  remain 
under  the  influence  of  the  magnet,  a  partial  oxidation  of  the  iron 
will  take  place,  and  we  shall  obtain  a  tolerably  compact  mass,  the 
composition  of  which  is  similar  to  that  of  natural  magnets,  and 
which,  also,  will  remain  permanently  magnetic. 


364        DIMINUTION    OF   MAGNETIC    FORCE    BY    DISTANCE. 

Diminution  of  Magnetic  Force  by  Distance. — Since  we  have  now 
learnt  to  know  the  magnetic  action  of  the  earth,  we  may  also  in- 
vestigate the  laws  by  which  the  strength  of  magnetic  attractions 
and  repulsions  diminishes  as  the  distance  increases.  It  will  be 
readily  understood  that  magnetic  actions,  like  all  other  actions 
emanating  from  one  point,  must  stand  in  inverse  relations  to  the 
squares  of  distance,  that  is  to  say,  at  2,  3,  or  4  times  the  distance, 
the  actions  will  be  4,  9,  or  16  times  less. 

When  we  endeavor  to  confirm  this  law  by  experiment,  we  labor 
under  the  peculiar  difficulty  of  being  unable  ever  to  try  the  expe- 
riment on  one  magnetic  pole,  without  having  to  contend  with  the 
counter  influence  of  the  other  pole ;  we  must,  therefore,  endeavor 
to  make  the  distance  between  the  poles  so  great  as  to  destroy  the 
disturbing  influence  exercised  by  the  one  over  the  other. 

Let  us  suppose  a  magnetic  needle  so  suspended  by  a  thread  of 
untwisted  silk,  as  to  be  able  to  oscillate  freely  in  a  horizontal  plane, 
while  it  is  sufficiently  protected  from  disturbing  currents  of  air. 

This  needle  must  be  first  left  to  oscillate  under  the  sole  influence 
of  terrestrial  magnetism.     Let  n  be  the  number  of  oscillations  ob- 
served in  a  minute,  and  m  the  horizontal  portion  of 
the  magnetic  terrestrial  force  acting  upon  it. 

Let,  now,  one  pole  of  a  highly  magnetized  steel 
bar  act  upon  the  needle.  This  steel  rod  is  to  be 
brought  into  the  magnetic  meridian  of  the  needle 
7i  5  in  a  vertical  position,  so  that  the  pole  s  of  the 
needle  is  to  be  turned  towards  the  pole  JVof  the  bar, 
on  which  it  will  act  attractively. 

The  bar  NS  must  be  so  large  that  the  distance 
s  JV*  may  be  as  small  as  possible,  in  comparison  with 
the  distance  s  S,  so  that  we  may  neglect  the  action  of  the  pole  S 
on  5,  without  committing  any  serious  error. 

If  we  designate  by  n'  the  number  of  oscillations  of  the  needle 
for  the  case,  where  the  pole  JVof  the  bar  NS  acts  upon  the  needle 
from  a  definite  distance,  and  call  the  force  accelerating  the  motion 
of  the  oscillating  needle^/*',  we  shall  have,  in  accordance  with  the 

ft  nt2 

former  experiment,  J-—  =  — . 

/         n 

Supposing  the  needle,  under  the  sole  influence  of  terrestrial 
magnetism,  to  make  15  oscillations  in  one  minute,  and  41  when 


DIMINUTION    OF    MAGNETIC    FORCE    BY    DISTANCE.        365 

pole  JV*  of  the  bar  is  removed  4  inches  from  the  needle,  we 

shall  have  i~  = 

f        152 

We  must  now  remove  the  bar  to  twice  as  great  a  distance,  so 
that  JV*  is  8  inches  from  the  needle,  and  then  observe  the  number 
of  oscillations ;  supposing  we  find  their  number  in  one  minute 

n"  =  24,  we  shall  have,  if  we  designate  asjf"  the  force  acting  in 

fi        242 
this  case  upon  the  needle,  J—  = 

f         152 

The  amount  f  is  evidently  the  sum  of  the  terrestrial  magnetic 
force,  and  of  the  attractive  force  exercised  by  the  pole  JV*  at  the 
distance  of  4  inches  upon  the  needle ;  the  latter  is,  therefore, 
evidently  f  — f.  In  like  manner,  the  attractive  force  exercised 
by  the  rod  at  a  distance  of  8  inches  upon  the  needle,  is  f"  — f. 
By  the  combination  of  the  two  latter  equations,  we  shall  have  the 
,,  f— f  412— 152  1456 

lowing  result:  Jj^f~  wH&"  351  =    '  *>1' 

This  experiment  shows,  therefore,  that  the  attractive  force  of  a 
magnetic  pole  acts  with  nearly  four  times  less  intensity  when 
removed  to  twice  the  distance. 

Weber  has  indirectly  proved  the  truth  of  this  proposition  by  his 
investigations,  not  merely  on  the  action  of  a  single  pole,  but  on 
that  of  the  whole  magnet  at  greater  distances.  He  has  shown 
that  if  a  magnetic  bar  be  small  in  comparison  with  the  distance 
at  which  it  acts,  the  total  action  of  the  magnet  must  diminish  in 
an  inverse  ratio  to  the  third  power  of  the  distance,  provided  the 
action  of  a  single  pole  really  stand  in  an  inverse  relation  to  the 
squares  of  the  distance. 

In  Fig:  339,  a  b  is  a  magnetic  bar,  1  decimetre  (3.93  in.)  in 
length,  whose  centre  is  10  decimetres  Fi  339 

(1  yd.  3  in.)  from  the  point  c;  the  dis-  c 

tance  of  the  pole  b  from  c  is,  therefore,     ^—£  I 

9,5,  (1  yd.,)  and  that  of  the  other  pole 

10,5dm,  (1  yd.  1  ft.  6  in.)  If,  now,  c  be  a  magnetic  pole,  and  if 
we  designate  as  1  the  force  with  which  the  poles  b  and  c  would 
attract  each  other,  supposing  them  to  be  ldm  from  one  another, 

the  attractive  force  will  be    A_  =         _,  if  the  attracting  action 

9,52       90,25 

of  the  pole  stand  in  an  inverse  relation  to  the  squares  of  distance. 
From  the  same  data,  the  value  of  the  repulsive  action  of  the  poles 

31* 


366       DIMINUTION   OF   MAGNETIC    FORCE   BY   DISTANCE. 

b  and  c  is  _  _;  the  total  action  exercised  by  the  mag- 

10,52      110,25 

net  a  b  upon  c  is,  therefore, 

1  1       _    20 

90^25        110,25       9950* 

If,  now,  we  remove  the  magnet  to  double  the  distance  of  c, 
that  is,  if  we  place  it  in  such  a  manner  that  the  middle  is  20th11 
from  c,  the  distance  b  c  being  equal  to  19,5,  the  distance  a  c  will 
be  20,5dm,  and,  consequently,  the  total  action  of  the  magnet  will 
be  as  follows : 

1  1  1  1  40 

19,52  ~~  20,52  =  380,25  ""  420,25  ^  159800* 
If,  therefore,  we  move  the  magnetic  bar  to  a  distance  of  20dm, 
instead  of  10dm  only,  its  action  must  diminish  in  the  relation  of 

to  ,  provided  the  action  of  each  separate  pole  stand 


9950       159800 

20 
in  an  inverse  relation  to  the  squares  of  distance.     But 


9950 
40  l          2  1598°  =  8,  at  double  the  distance, 


159800       995     15980         1990 

the  total  action  of  the  magnet  is  8  times  weaker,  and  8  is  the 

third  power  of  2. 

What  we  have  shown  here  by  particular  examples,  may  also 
be  generally  proved,  as  it  admits  of  a  general  proof  that  the  total 
action  of  a  magnet  must  be  in  an  inverse  ratio  to  the  third  power 
of  the  distance,  if  the  action  of  one  single  pole  stand  in  an  inverse 
relation  to  the  squares  of  the  distance. 

We  will  now  adduce  an  experiment,  by  which  the  total  action 
of  a  magnetic  bar  is  shown  to  be  as  the  third  power  of  the  dis- 
tance, provided  the  magnet  be  small  in  comparison  with  this 
distance. 

A  bar  3  feet  in  length,  and  divided  into  inches,  must  be  so  laid 
that  its  direction  may  be  at  right  angles  to  the  magnetic  meridian. 
A  small  compass  is  then  placed  in  the  middle,  as  represented  in 
Fig.  340.  The  needle  of  this  compass  will  stand  at  0,  if  the 
magnetic  terrestrial  force  be  the  only  one  acting  upon  it.  If, 
however,  a  magnet  be  laid  sideways  upon  the  rod,  the  needle  will 
be  turned  aside ;  and  then  this  deviating  force  will  be  proportional 
to  the  tangent  of  the  angle  of  deviation. 

Let  us  now  lay  a  magnetic  bar  3  inches  in  length,  in  such  a 


DIMINUTION    OF    MAGNETIC    FORCE    BY   DISTANCE.        367 

manner  (as  seen  in  Fig.  340),  that  its  middle  may  be  15  inches 
from  the  middle  of  the  compass.  In  such  an  experiment  the 
deviation  will  amount  to 


If  the  magnetic  bar  n  s  be  now  placed  in  such  a  manner  that 
its  centre  is  10  inches  from  the  centre  of  the  compass,  the  devia- 
tion will  amount  to  35J°. 

The  distances  here  are  to  each  other  as  10  to  15,  or  as  2  to  3  ;  the 
tangents  of  the  angles  of  deviation  must,  therefore,  be  as  23  to  33, 

27 

or  as  8  to  27  ;  and  here  we  shall  have  —  =  3,375. 

8 

ut  the  tangent  of  11J°  =  0,2034,  the  tangent  of  35  £°  = 
0,7115,  and  !?']?***?  =  3,49  ;  the  tangent  of  the  angles  of  devia- 


tion  are,  therefore,  very  nearly  as  8  to  28,  or  as  the  third  powers 
of  the  distances. 


368 


ELECTRICITY. 


PART  II. 

OF     ELECTRICITY. 

CHAPTER    I. 


Fig.  341. 


OF  ELECTRICAL  ACTIONS. 

There  are  bodies  which,  by  friction,  acquire  the  property  of 
attracting  Light  Bodies. — We  may  easily  convince  ourselves  that 
bodies,  in  their  ordinary  condition,  do  not  possess  the  property  of 
attracting  light  bodies,  as  gold-leaf,  sawdust,  paper-cuttings, 
balls  of  the  pith  of  the  elder,  &c. ;  but  if  we  rub  a  glass  rod,  or 
a  piece  of  sulphur,  or  sealing-wax,  or  amber,  &c.,  with  a  woollen 
or  silk  substance,  these  bodies  will  immediately 
acquire  this  remarkable  property.  This  attrac- 
tive force  is  so  great,  that,  even  at  the  distance 
of  more  than  a  foot,  light  bodies  are  drawn 
towards  the  attracting  body  (Fig.  341).  The 
cause  of  this  phenomenon  is  called  Electricity. 

We  may  make  use  of  the  electrical  pendulum,  (represented  in 
Fig.  342),  in  order  to  ascertain  whether  a 
body  will  become  electrical  by  friction.  This 
apparatus  consists  of  a  small  ball,  made  of 
the  pith  of  the  elder,  and  suspended  to  a 
fine  linen  thread.  If  we  would  test  a  body, 
we  bring  it  towards  the  ball;  if  it  be  not 
attracted,  it  is  either  non-electric,  or  too 
slightly  electric  to  produce  any  effect. 

By  the  aid  of  the  electric  pendulum,  it 
may  be  shown,  that  all  resins,  amber,  sul- 
phur, and  glass,  become  strongly  electric  by  friction;  the  precious 
stones,  wood,  and  charcoal,  seldom  give  the  slightest  indications 


Fig.  342. 


CONDUCTORS    AND    NON-CONDUCTORS.  369 

of  attraction;  metals  do  not  appear,  at  first  sight,  to  admit  of 
being  made  electric,  for  we  do  not  perceive  the  least  trace  of 
attraction  in  this  apparatus  on  forcibly  rubbing  a  metal  rod.  All 
bodies  thus  fall  under  two  great  classes ;  that  is,  such  as  become 
electric  by  friction,  and  such  as  do  not  thus  acquire  an  electric 
condition.  The  former  we  term  idioelectric,  the  latter  anelectric 
bodies. 

This  division  is  founded,  however,  upon  an  erroneous  view, 
for  it  has  been  found  that  all  bodies,  even  metals,  can  be  made 
electric  by  friction,  and,  although  we  may  be  unable,  in  many 
bodies,  to  perceive  any  trace  of  electricity  from  friction,  the  cause 
depends  upon  other  circumstances,  of  which  we  shall  soon  treat. 

Conductors  and  Non- Conductors. — It  was  formerly  supposed 
that  the  bodies,  designated  by  the  term  anelectric,  could  not,  by 
any  means,  be  brought  into  an  electric  condition.  In  1727,  ex- 
periments were  made,  with  a  glass  tube,  open  at  both  ends,  on 
this  subject,  by  Gray,  an  English  natural  philosopher.  He  wanted 
to  see  whether  it  would  become  electric,  if  closed  up  at  both  ends 
by  a  cork  stopper.  At  that  epoch,  science  was  so  little  advanced, 
that  experiments  were  made  at  random,  there  being  neither  hypo- 
thesis nor  theory  by  which  to  conduct  the  course  of  investigation. 
To  his  great  astonishment,  Gray  found  that  the  stoppers  them- 
selves had  become  electric,  although  cork  belonged  to  the  sub- 
stances reckoned  anelectric.  A  metal  wire,  passed  through  the 
cork,  became  electric,  independently  of  the  length  at  which  it 
was  used ;  having  successively  carried  the  electrical  rod  to  the 
first,  second,  and  third  stories  of  his  house,  and  let  the  metal  wire 
descend  to  the  ground.  He  rubbed  the  glass  tube,  while  a  friend 
brought  light  bodies  to  the  lower  end  of  the  wire,  on  which  they 
were  instantly  attracted  by  it.  It  follows  from  thence,  that 
metals  have  the  property  of  assuming,  and  imparting  to  other 
bodies,  an  electric  condition.  The  same  property  is  possessed, 
however,  by  all  anelectric  bodies ;  and,  hence,  they  have  been 
termed  conductors  of  electricity.  Idioelectric  bodies,  on  the  other 
hand,  are  non-conductors;  for  when,  by  friction,  we  make  one 
end  of  a  glass  tube  electric,  the  other  end  exhibits  no  trace  of 
attraction. 

We  may  easily  demonstrate  this  fundamental  truth  by  the  aid 
of  an  electrifying  machine,  of  which  we  may  make  use  to  deve- 
lop electricity,  without  knowing  the  principle  of  its  construction. 


370  CONDUCTORS    AND    NON-CONDUCTORS. 

The  conductor  of  the  machine  is  a  metallic  body,  which  is  made 
electric.  If  we  bring  in  contact  with  the  conductor,  when  in  an 
electrified  condition,  a  metal  wire,  suspended  by  a  silk  thread,  or, 
better  still,  some  cylindrical  metal  body,  standing  on  a  glass 
pedestal,  the  metal  will  be  electrified  through  its  whole  extent ; 
as  soon,  however,  as  it  be  connected  with  the  earth,  by  means  of 
any  good  conductor,  all  its  electricity  will  instantly  disappear. 

From  this  it  follows  that  silk  threads  and  glass  rods  are  non- 
conductors of  electricity  insulators.  A  conductor  of  electricity 
can,  therefore,  only  remain  electric  as  long  as  it  is  insulated,  that 
is,  surrounded  by  perfect  non-conductors.  The  air  must  be  an 
insulator,  since,  if  it  were  not  so,  electricity  would  be  instantly 
withdrawn  by  the  atmosphere  from  metals.  Water  and  steam  are 
good  conductors,  consequently,  when  the  atmosphere  is  damp,  the 
electricity  will  soon  be  lost,  which,  in  a  dry  condition  of  the  air, 
would  have  adhered  to  an  insulated  conductor  for  a  long  period  of 
time. 

The  human  body  is  likewise  a  good  conductor.  If  we  stand 
on  the  ground,  and  lay  hold  of  the  conductor  of  an  electrifying 
machine,  all  the  electricity  evolved  from  turning  the  machine  will 
immediately  escape  ;  but,  if  we  stand  upon  a  bad  conductor,  as  a 
piece  of  resin,  the  whole  body  will  become  electric.  This  ex- 
plains the  reason  of  a  metallic  rod  not  becoming  electric  by  fric- 
tion when  we  hold  it  in  the  hand ;  all  the  electricity  obtained  by 
the  friction  being  immediately  given  off  to  the  human  body,  and 
thence  to  the  ground. 

The  best  insulators  may  become  conductors  if  they  be  covered 
with  condensed  vapor.  It  is,  therefore,  of  the  greatest  import- 
ance to  the  successful  result  of  electrical  experiments,  that  the 
glass  feet,  resin  rods,  &c.,  used  for  insulating  a  conductor,  should 
be  well  dried  by  warmth  and  friction. 

Instead  of  dividing  bodies  into  conductors  and  non-conductors, 
we  ought,  more  correctly  speaking,  to  term  them  good  and  bad 
conductors,  since  there  do  not  exist  any  absolute  non-conductors ; 
shell-lac,  and  more  especially  resin,  silk,  and  glass  are  the  worst 
conductors  we  have ;  while,  on  the  contrary,  metals  constitute 
the  best  conductors. 

Of  the  two  kinds  of  Electricity. — Let  us  take  a  simple  electrical 
pendulum  (see  Fig.  342),  whose  nob  is  suspended  to  a  silk  thread. 
If  we  now  bring  a  rubbed  glass,  or  shell-lac  rod  to  the  pendulum, 


ELECTRICITY    OF    FLUIDS,    ETC.  371 

the  pith  ball  will  be  strongly  attracted,  then  touch  the  rod,  and, 
after  adhering  to  it  for  some  minutes,  will  be  repelled.  This  re- 
pulsion depends  upon  the  electricity  communicated  to  the  ball  by 
contact  with  the  rod,  for,  on  touching  it  with  the  hand,  and  then 
bringing  it  back  to  its  natural  condition,  it  will  be  again  attracted, 
and  repelled  after  a  second 

Fig.  343. 

time  being  brought  into  con- 
tact. 

It  follows  that  the  repelled 
ball  is  really  electric,  from  its 
being  attracted  by  bodies  in 
their  natural  condition, provided 
we  make  choice  of  conductors 
for  the  experiments.  If  we  take 
two  insulated  pendulums,  one 
of  which  has  been  made  electric  by  contact  with  a  glass  rod 
rubbed  with  silk,  and  the  other  by  a  rod  of  shell-lac  rubbed  with 
fur  or  flannel,  we  shall  perceive  the  following  remarkable  pheno- 
mena. The  ball  that  has  been  repelled  by  the  glass  rod  will  be 
attracted  by  the  shell-lac  rod,  while  the  one  repelled  by  the  shell- 
lac  will  be  attracted  by  the  glass.  The  electricity  evolved  from 
glass,  consequently,  is  not  identical  with  that  evolved  from  resins, 
since  the  one  attracts,  and  the  other  repels. 

These  two  kinds  of  electricity  have  received  the  names  of  vitre- 
ous and  resinous  electricity.  The  former  is  also  termed  positive, 
and  the  latter  negative.  The  discovery  of  these  two  different  kinds 
of  electricity  was  made  by  Dufay  in  the  year  1773. 

Of  the  Electric  Fluids,  and  the  Natural  Condition  of  Bodies. — 
Owing  to  the  rapidity  with  which  electricity  distributes  itself 
through  conductors,  it  has  been  concluded  that  it  must  be  a  body 
endowed  with  remarkable  powers  of  motion,  and,  from  the  laws  of 
vitreous  and  resinous  electricity,  it  has  been  further  assumed  that 
there  must  be  two  electric,  as  there  are  two  magnetic,  fluids. 
When  these  two  fluids  are  united  in  one  body,  and  when  they 
mutually  neutralize  each  other  in  that  body,  the  body  is  in  its  na- 
tural condition.  If,  however,  the  two  electricities  are  decomposed 
in  a  body,  it  will  become  electric,  positively,  if  the  vitreous  elec- 
tricity, and  negatively,  if  the  resinous  electricity  predominates. 
There  exists,  however,  an  essential  difference  between  the  electric 
and  magnetic  fluids ;  the  latter  being,  as  it  were,  enclosed  in  the 


372  ELECTRICITY    OF    FLUIDS,    ETC. 

magnetic  particles,  while  the  electric  fluid  can  pass  freely  from 
one  body  to  another. 

If  +  electricity  be  given  off  by  friction  in  a  body,  —  electricity 
must  be  developed  in  an  equal  degree.  We  may  show  this  by  a 
simple  experiment.  If  we  rub  together  two  discs  of  different 
substances,  which  are  insulated  by  glass  rods,  they  will  exhibit  no 
trace  of  electricity  so  long  as  they  rest  on  each  other; 
Flg'  344'  as  soon,  however,  as  they  are  separated,  the  one  will 
be  found  to  be  positively  electric,  and  the  other  nega- 
tively so,  and  in  an  equal  degree.  This  experiment 
is  best  exemplified  where  one  disc  is  of  glass,  and 
the  other  of  some  wood  covered  with  leather,  which 
has  been  rubbed  over  with  amalgam.  We  may, 
also,  take  discs  of  any  other  substance,  such  as  resin, 
metal,  &c.,  covering  them  with  different  materials,  to 
vary  the  experiment,  as,  for  instance,  with  cloth, 
silk,  paper,  &c. 

Since  a  body  in  its  natural  condition  contains  both  electricities 
in  equal  quantities,  there  is  no  reason  to  suppose  that  it  is  disposed 
to  take  up  and  retain  either  kind  in  particular ;  it  may,  therefore, 
become  positively  or  negatively  electric,  according  to  the  sub- 
stance with  which  we  rub  it.  Glass,  for  instance,  becomes  posi- 
tively electric  when  rubbed  with  wool  or  silk,  and  negatively  so, 
when  rubbed  with  cat-skin.  In  order,  therefore,  to  designate  the 
fluids  distinctly,  we  must  thus  express  ourselves.  Positive  or  -f 
electricity  is  that  kind  of  electricity  assumed  by  glass,  on  the 
latter  being  rubbed  with  wool  or  silk  ;  negative  or —  electricity,  on 
the  contrary,  is  that  kind  developed  by  resins  rubbed  with  cat-skin, 
wool  or  silk.  If  we  suppose  a  list  of  different  bodies  to  be  so 
drawn  up,  that  each  one,  when  rubbed  with  all  those  succeeding 
it,  becomes  positively  a  -f  electric,  we  shall  soon  remark  how  the 
smallest  change  of  circumstances  alters  the  order  of  this  series. 
A  change  of  temperature,  for  instance,  may  oblige  us  to  move 
the  body  upwards  or  downwards  in  the  series.  The  same  action 
is  often  produced  by  making  the  surface  of  a  body  rougher  or 
smoother.  The  color,  the  arrangement  of  the  molecules  or  fibres, 
or  simply  a  more  or  less  strongly  applied  pressure,  may  produce 
similar  phenomena.  A  black  silk  ribbon,  for  instance,  will  be 
negatively  electrified  when  rubbed  with  a  white  silk  ribbon. 
Even  on  rubbing  two  pieces  of  the  ribbon  crosswise  together,  the 


COMMUNICATION   OF    ELECTRICITY.  373 

one  used  for  rubbing  will  become  positively  electrified,  and  the 
other  negatively  so.  Again,  on  rubbing  a  polished  glass  disc 
upon  a  ground  glass  disc,  they  will  likewise  become  oppositely 
electric,  &c. 

Communication  of  Electricity . — Free  electricity  may  pass  from 
one  body  to  another,  as  well  by  immediate  contact,  as  at  great 
distances,  the  communication  depending  upon  the  capacity  of  the 
body  for  conducting  electricity  and  the  amount  of  its  surface. 

On  being  brought  into  contact  with  an  electrified  body,  bad 
conductors  only  take  up  electricity  at  the  place  of  contact  without 
its  being  transmitted  over  their  whole  extent.  If,  on  the  other 
hand,  we  touch  an  electrified  insulator,  it  will  lose  its  electricity 
only  at  the  spot  touched,  the  remainder  of  its  surface  continuing 
electric  as  before.  This  may  be  easily  seen  by  means  of  a  rubbed 
piece  of  sealing-wax,  or  a  glass-rod.  The  case  is  very  different 
with  good  conductors.  When  touched  at  one  point  by  an  electric 
body,  the  electricity  will  be  diffused  over  the  whole  conductor, 
and  if  we  bring  an  insulated  electrified  conductor  into  contact 
with  the  earth,  it  will  immediately  lose  its  electricity. 

Electricity  may  also  pass  from  one  body  to  another,  without 
immediate  contact,  and  here  we  remark  the  extraordinary  pheno- 
menon of  the  electric  spark.  On  bringing  a  metal  rod,  or  one  of 
the  knuckles,  near  a  rubbed  glass  or  shell-lac  rod,  we  see  a  brightly 
shining  spark  emitted,  and  hear  a  crackling  noise.  If  the  elec- 
trified body  be  an  insulated  metal  of  considerable  surface,  as  the 
conductor  of  the  electrifying  machine,  the  sparks  will  be  more 
vivid,  passing,  under  some  circumstances,  to  a  distance  of  12 
inches ;  their  light  will  then  be  dazzlingly  bright,  and  the  noise 
accompanying  them  very  loud. 

Otto  von  Guericke,  the  inventor  of  the  air-pump,  was  the  first 
who  observed  electric  sparks.  Subsequently  Dufay  proved  to  the 
astonishment  of  every  one,  that  they  might  be  drawn  from  the 
human  body  as  from  the  conductor  of  a  machine. 

To  make  this  experiment,  we  must  stand  upon  a  piece  of  resin, 
or  a  stool  with  glass-legs  (an  insulated  stool),  and  bring  our  body 
into  contact  with  the  conductor  of  the  machine.  On  turning  the 
machine  we  shall  be  conscious  of  a  peculiar  sensation  upon  the 
skin,  especially  the  face,  as  though  we  were  entangled  in  a  web. 
The  hair  on  the  head  will  stand  on  end.  If,  now,  the  electrified 
human  body  be  brought  into  contact  with  an  insulated  conductor, 
32 


374  COMMUNICATION   OF   ELECTRICITY. 

as  another  person,  for  instance,  and  the  latter  advance  the  knuckles, 
a  spark  will  be  emitted,  which  will  be  felt  in  proportion  to  the 
distance  it  has  traversed. 

Electricity  always  distributes  itself  according  to  the  amount  of 
surfaces  on  passing  from  one  insulated  conductor  to  another;  in 
order,  therefore,  to  deprive  an  insulated  conductor  of  all  its  elec- 
tricity, we  must  bring  it  into  contact  with  another,  having  an 
infinitely  larger  area,  as,  for  instance,  with  the  ground,  for  it  is 
thus  brought  in  contact  with  the  whole  earth's  surface,  in  which 
its  electricity  is  wholly  lost  from  being  regularly  distributed  over 
so  vast  an  extent.  If  we  were  to  bring  an  insulated  electrified 
metal  ball  into  contact  with  another  equally  large,  likewise  insu- 
lated and  non-electric,  the  former  would  lose  exactly  half  its 
electricity.  On  bringing  an  insulated  metal  ball  near  the  con- 
ductor of  an  electrifying  machine,  only  faint  sparks  will  be  drawn 
from  the  machine  by  means  of  a  non-insulated  conductor. 

A  taper  that  has  been  just  extinguished  may  be  relighted  by 
an  electric  spark.     In  like  manner,  ether  and  alcohol  may  be 
influenced  by  the  electric  spark ;  to  effect  this  we  must  pour  the 
fluid  into  a  metallic  vessel,  and  bring  near  to  the  surface  of  the 
fluid  the  electrified  body  from  which  the  sparks  are  to  be  emitted. 
The  electric  pistol  is  represented  in  Fig.  345.     It  is  a  small 
Fig  345  metallic  vessel  secured  by  a  cork  stopper.    A 

metal  wire  terminating  in  two  small  balls  b  and 
V  penetrates  into  the  vessel  without  being  in 
contact  with  the  wall.  For  the  purpose  of  effect- 
ing this,  the  wire  is  fastened  with  sealing-wax 
into  a  glass  tube  t  tf,  and  this  cemented  into  an 
aperture  of  the  lateral  wall.  The  electric  spark 
conducted  by  the  wire  passes  from  the  ball  b'  to 
the  opposite  wall.  If,  now,  the  vessel  be  filled 
with  an  explosive  gas,  as  a  mixture  of  hydrogen 
and  atmospheric  air,  the  spark  will  produce  such  an  effect  by  the 
explosion  of  the  machine  as  to  cause  the  stopper  to  be  propelled 
with  a  loud  report. 


ELECTRICITY    BY    INDUCTION. 


375 


CHAPTER    II. 


Fig.  346. 


ELECTRICITY  BY  INDUCTION. 

WE  have  seen  that  each  of  the  electric  fluids  repels  the  like 
fluid  and  attracts  the  opposite.  This  attraction  and  repulsion  not 
only  show  themselves  in  the  decomposed 
fluids,  but  on  those  still  in  combination, 
whence  it  happens  that  the  combined  electri- 
cities of  a  body  in  a  natural  condition  are  dis- 
turbed by  the  approximation  of  an  electric 
body.  Let  a  ring  of  metal  be  attached  to  an 
insulated  hook,  and  have  two  metallic  threads 
passing  through  it,  at  the  end  of  which  are  two 
pith  balls.  On  the  approach  of  an  elastic 
body  r,  the  balls  will  start  away  from  each 
other  even  when  r  is  very  far  removed,  and 
no  spark  is  transmitted  to  them.  This  di- 
vergence increases  the  nearer  we  bring  r. 

It  is  evidently  not  the  effect  of  transmitted 
electricity,  for  the  pendulums  fall  together  the  moment  we  remove 
r.     The  electricities  which  were  combined  in  the  metallic  ring 
and  the  pendulums  before  the  approximation  of  r,  have 
been  separated ;  that  kind  of  electricity  which  is  like 
that  of  r,.  is  repelled  towards  the  balls,  whilst  the 
opposite  is  attracted  to  the   ring.     If,  therefore,  the 
electric  body  r  is  a  rubbed  rod  of  resin,  that  is  — 
electric,  the  ring  will  become  +  electric,   and  the 
balls  — . 

We  may  demonstrate,  by  means  of  a  test  disc,  that 
the  two  kinds  of  electricity  are  really  distributed  in  the 
way  indicated.  A  test  disc  is  made  of  gold  leaf,  or  gold 
paper,  from  1  to  2  centimetres  in  diameter,  (^  to  £  inch) 
and  fastened  to  a  long  rod  of  shell-lac,  or  thin  glass  rod 
covered  with  varnish.  If  we  touch  the  ring  with  this 
iisc  whilst  the  negatively  electric  body  r  is  so  near  it 
:hat  the  pendulums  diverge,  the  test  disc  will  be  charged  with 


Fig.  347. 


376  ELECTRICITY   BY   INDUCTION. 

the  electricity  of  the  ring,  the  nature  of  which  we  shall  learn  by 
bringing  a  simple  electric  pendulum  near  the  disc  to  which  elec- 
tricity has  already  been  imparted.  Supposing  that  the  simple 
pendulum  has  been  made  +  electric  by  contact  with  a  glass  rod, 
it  will  be  repelled  by  the  test  disc,  since  the  latter,  as  well  as  the 
ring,  is  +  electric. 

This  experiment  may  be  conducted  as  follows.  We  must 
attach  to  each  hook-like  extremity  of  a  metal  rod,  supported  on 
an  insulated  glass  stand,  a  couple  of  pendulums  having  conduct- 
ing threads  made  either  of  slender  metallic  wire  or  linen  thread. 
Both  these  double  pendulums  will  diverge  on  the  approach  of  an 
electric  body  r,  the  balls  of  the  one  pair  being  charged  with  +, 
and  the  other  with  —  electricity.  On  removing  the  body  r,  the 

Fig.  348. 


pendulums  will  again  approach  each  other,  because  the  separated 
electricities  then  immediately  combine. 

A  body  electrified  by  induction,  acts  on  its  part  again,  by  induc- 
tion upon  other  bodies  brought  sufficiently  near  it,  that  is,  within 
its  sphere  of  activity,  which  may  extend  to  a  considerable  dis- 
tance. A  glance  at  Figs.  349  to  352,  will  suffice  to  show  the 
arrangement  that  must  be  made,  in  order  to  demonstrate  the  truth 
of  this  by  experiment ;  m  is  the  conductor  of  an  electrifying  ma- 
chine, c  one  insulated  metallic  cylinder,  c'  another,  b  a  metallic 
ball,  and  bf  a  pith-ball. 

If,  by  means  of  a  conducting  medium,  we  bring  an  insulated 
conductor  (electrified  by  induction)  into  contact  with  the  ground, 


ELECTRICITY   BY   INDUCTION. 


377 


while  the  electric  body  still  acts  inductively  by  its  approximation, 
all  the  repelled  electricity  will  be  carried  off  by  the  earth,  and 


Fig.  349. 


Fig.  350. 


Fig.  351. 


Fig.  352. 


the  insulated  conductor  will  only  remain  charged  with  the  elec- 
tricity attracted  from  the  inductive  body  r.  If  we  again  destroy 
the  communication  with  the  earth,  and  remove  r,  the  insulated 
conductor  will  be  charged,  throughout  its  whole  extent,  with  the 
same  electricity. 

The  apparatus  in  Fig.  346,  made  in  a  somewhat  different  form, 
serves  admirably  as  an  electroscope.  Care  must  be  taken  that 
the  pendulums  are  secured,  in  a  glass  vessel,  in  order  to  hinder 
the  injurious  interference  of  external  influences,  as  currents  of 
air,  &c.,  besides  which,  the  conducting  system  must  be  carefully 
insulated.  The  pendulums  may  be  formed  of  blades  of  straw, 
and  balls  made  of  the  elder  pith,  suspended  to  metallic  threads, 
or  of  metallic  plates. 

Fig.  353  represents  a  gold  leaf  electrometer.  A  glass  tube 
passed  through  the  opening  of  the  glass  vessel,  having  a  metal 
rod,  covered  with  shell-lac  varnish,  fastened  to  it,  and  penetrating 


Fig.  353. 


Fig.  354. 


378 


ELECTRICITY    BY    INDUCTION. 


into  the  vessel,  while  the  gold  leaf  pendulums  are  fastened  to  the 
lower  extremity  of  this  metallic  rod ;  a  metal  plate  is  screwed  on 
the  top. 

In  order  to  be  able  to  measure  the  divergence  of  the  pendu- 
lums, a  graduated  arc  is  either  introduced  into  the  interior  of  the 
glass  vessel ;  or,  instead  of  this,  a  glass  box  is  used,  as  repre- 
sented in  Fig.  354,  on  the  side  of  which  the  graduated  arc  is 
attached. 

The  experiment,  shown  in  Fig.  346,  may  also  be  made  by  the 
above  delineated  electroscope.  If  we  place  above  it  an  electric 
body,  as  a  rubbed  glass  rod,  for  instance,  the  pendulums  will 
diverge ;  the  nature  of  the  electricity  collected  in  the  upper  plate, 
may  be  ascertained  by  means  of  the  test  disc,  it  being  the  con- 
trary to  that  of  the  approximating  body  r, 

If  we  wish  to  examine  into  the  nature  of  the  electricity  of  any 
body,  the  electroscope  must  be  charged  beforehand  with  a  kind  of 
electricity  with  which  we  are  acquainted,  and  this  may  be  done 
by  bringing  a  body  r,  whose  electricity  is  known,  near  the  appa- 
ratus, and  touching  the  plate  with  the  finger.  By  this  means  all 
the  repelled  electricity  is  carried  off,  there  remaining  only  the 
portion  attracted  and  accumulated  upon  the  plate.  It  is  to  a  cer- 
tain extent  combined,  that  is  to  say,  it  cannot  escape,  being  at- 
tracted by  ry  on  which  account  the  pendulums  do  not  diverge ; 
immediately,  however,  on  removing  the  finger  and  the  body  r+ 
Fi  355  the  pendulums  will  diverge  as  the  electricity 

which  was  combined  with  the  plate  by  the 
body  r,  disperses  itself  freely  over  the  whole 
insulated  system,  consequently  also  over  the 
pendulums.  The  electricity  with  which  the 
electroscope  is  in  this  manner  charged  must 
naturally  be  contrary  to  that  of  the  body  r\ 
thus,  if  we  want  a  negative  charge  we  may 
make  use  of  a  glass  rod  rubbed  with  silk, 
since  this  is  +  electric. 

If  we  bring  an  electric  body  to  the  charged 
electroscope,  the  divergence  of  the  pendu- 
lums will  either  be  increased  or  diminished 
in  consequence.  It  will  be  increased  if  the 
electricity  of  the  body  to  be  examined,  be 
the  same  as  that  imparted  to  the  apparatus, 


ELECTRICITY   BY   INDUCTION. 


379 


for  by  its  approximation,  the  electricities  of  the  electroscope  are 
more  thoroughly  decomposed  than  was  the  case  before,  and  more 
electricity  of  the  same  kind  as  that  already  in  the  pendulums,  is 
imparted  to  them,  when  their  divergence  must  consequently  in- 
crease. 

If  the  approximated  body  be  of  the  contrary  electricity  to  that 
imparted  by  the  electroscope,  the  divergence  diminishes  as  the 
electricity  is  withdrawn  from  the  pendulum  and  drawn  into  the 
plate.  Whatever  be  the  electricity  with  which  the  apparatus  is 
charged,  there  will  still  be  undecomposed  electricities  in  the  ap- 
paratus, which  will  be  decomposed  by  the  approximated  body:  if 
the  electricity  in  the  latter  be  contrary  to  that  present  in  the  elec- 
troscope, the  amount  of  electricity  already  developed*  will  be 
drawn  into  the  plate,  while  the  other  will  be  urged  into  the  pen- 
dulums, the  divergency  of  which  must  therefore  diminish.  At  a 
definite  distance  from  the  approximated  body,  the  electricities  will 
neutralize  each  other  in  the  pendulums,  which  will  then  fall 
closely  together.  If  the  body  to  be  tested  be  brought  still  nearer, 
the  pendulums  will  again  diverge,  but  with  electricity  of  a  kind 
contrary  to  that  which  made  them  previously  diverge. 

The  divergence  of  the  pendulums  likewise  diminishes  on  bring- 


Fig.  356. 


Fig.  357. 


Fig.  358. 


Fig.  359. 


ing  a  non-conductor  near  the  charged  electroscope.    This  follows 
as  the  necessary  consequence  of  the  laws  of  electric  induction. 

On  uniting  two  similar  electroscopes  by  an  insulated  conductor, 
and  bringing  an  electric  body  r  near  one  of  them,  the  pendulums 
in  both  jars  will  diverge,  the  one  from  +,  and  the  other  from  — 
electricity.  On  removing  the  connecting  conductor  (we  must,  of 


380  THE    ELECTROPHORUS. 

course,  hold  it  by  the  insulated  handle)  the  pendulums  will  not 
meet  again,  even  after  the  removal  of  the  body  r  effecting  the 
induction,  owing  to  the  separated  electricities  having  no  way  by 
which  they  can  pass  back  to  each  other.  We  may  know  that  the 
electricities  in  both  apparatuses  are  of  different  natures,  by  bring- 
ing the  same  electric  body  first  to  the  one,  and  then  to  the  other 
electroscope,  when  we  shall  see  them  diverge  in  the  one  case,  and 
collapse  in  the  other. 

The  above-described  phenomena  of  attraction  can  also  be  ex- 
plained by  the  laws  of  electric  induction.  If  a  body  in  a  natural 
condition  be  brought  near  one  that  is  electric,  its  electricities  will 
be  decomposed.  This  will  also  be  the  case  with  the  cork  ball  of 
the  simple  electric  pendulum.  If  it  be  suspended  by  a  silk  thread, 
the  repelled  electricity  cannot  escape  from  the  ball,  but  will  be 
urged  to  the  reverse  side  of  the  ball,  whilst  the  attracted  electri- 
city will  be  accumulated  in  the  front.  As  the  attracted  electricity 
is  nearer  to  the  body  from  which  the  action  proceeds,  the  attrac- 
tion will  be  stronger  than  the  repulsion ;  the  force  urging  the  ball 
towards  the  electric  body  will  be  equal  to  the  difference  of  these 
two  opposite  forces;  a  very  small  removal  of  the  electric  body 
will,  therefore,  be  followed  by  attraction.  The  action  will  be  far 
stronger  where  the  ball  is  suspended  to  a  conducting  thread,  as 
in  that  case  the  repelled  electricity  can  escape,  and  the  attraction 
will  consequently  not  be  weakened. 

A  ball  of  shell-lac  is  not  attracted  by  the  approximation  of  an 
electric  body,  as  the  approximated  body  is  only  capable,  with 
difficulty,  of  causing  induction.  This  phenomenon  resembles 
what  maybe  seen  in  the  case  of  a  magnet,  which  easily  occasions 
a  magnetic  induction  in  a  piece  of  soft  iron,  but  can  only  effect 
the  same  in  a  piece  of  steel  with  extreme  difficulty. 

The  Electrophorus  is  one  of  the  most  important  electrical  ap- 
paratuses, and  may,  in  many  cases,  replace  the  electrifying  ma- 
chine.    It  consists  of  a  cake  of  resin,  which,  as  seen  in  Fig.  360, 
is  fused  in  a  plate  of  metal,  or  a  cake  of  resin  simply  laid 
Fig.  360.  upon  a  somewhat  larger  metal  plate. 

It  is  very  important  that  the  surface  of 
the  cake  of  resin  should  be  as  smooth 
as  possible.  On  this  cake,  the  surface 
of  which  has  been  made  negatively  elec- 
tric by  striking  it  with  a  fox-tail  or 
cat's-skin,  we  place  a  metal  cover  pro- 


THE   ELECTRIFYING  MACHINE.  381 

vided  with  an  insulated  handle  m.  The 

Fig.  361. 

electricity  of  the  cake  of  resin  acts 
inductively  upon  the  two  electricities 
hitherto  combined  in  the  cover,  the  -f 
electricity  is  attracted,  the  —  electri- 
city repelled ;  the  former  will,  there- 
fore, accumulate  in  the  lower  part  of  the  cover,  and  the  latter  in 
its  upper  part.     On  bringing  the  knuckle  of  the  finger  near  the 
cover,  a  spark  will  be  elicited,  and,  on  touching  the  cover  with 
the  finger,  all  the  —  electricity  will  escape,  -f  electricity  alone  re- 
maining, which,  however,  is  combined  with  the  —  electricity  of 
the  cake  of  resin,  as  long  as  the  cover  is  on ;  but,  if  this  be  re- 
moved, the  4-  electricity  will  be  liberated,  and  we  may  draw  a 
spark  of  -f  electricity  from  the  cover. 

If  the  cake  of  resin  be  laid  directly  upon  a  metal  plate,  there  is 
less  fear  of  the  cake  cracking  by  the  change  of  temperature,  as 
may  easily  be  the  case,  owing  to  the  unequal  expansion  of  the 
metal  and  resin  in  melted  cakes.  The  best  substance  for  an 
electrophorus,  is  shell-lac  mixed  with  Venice  turpentine. 

Zinc  may  be  used  as  the  material  for  constructing  the  metallic 
plate  on  which  the  resin  cake  is  laid.  The  cover  is  generally  of 
brass,  and  has  its  edge  rounded  off.  Covers  of  glass,  wood,  or 
pasteboard  answer  the  purpose,  however,  when  coated  with  tin- 
foil ;  but  care  must  be  taken  to  have  the  under  surface  lying  on  the 
cake  of  resin  as  smooth  as  possible.  In  the  place  of  an  insulated 
glass  handle,  the  cover  may  be  fastened  with  three  silk  cords. 

The  Electrifying  Machine  consists  of  a  rubbing  body,  a  rubber, 
and  an  insulated  conductor. 

The  rubbing  body  is  generally  a  horse-hair  cushion.  The  rub- 
bing surface,  a  piece  of  leather  covered  with  amalgam. 

The  body  rubbed  is  a  glass  disc  or  cylinder. 

The  insulated  conductor  is  generally  a  system  of  hollow  con- 
ductors, made  of  brass  plate,  spherically  rounded  at  the  extremi- 
ties, and  supported  by  glass  legs,  varnished  with  shell-lac. 

Many  different  forms  have  been  given  to  the  electrifying  ma- 
chine; the  one  most  in  use  is  represented  in  Fig.  362.  The  dia- 
meter of  the  glass  plate  a  varies  from  20  to  60  inches.  An  axis 
passes  through  an  opening  in  its  centre,  and  supports  the  winch  b. 
The  pillars  d  bear  the  plate,  and  likewise  the  couple  of  pairs  of 
cushions  e  and  ef,  which  rub  the  plate  from  the  edge  to  about  J 


382 


THE    ELECTRIFYING   MACHINE. 


or  J  of  its  diameter.  The  conductor  fgf  is  insulated  by  the 
columns  A,  and  terminates  in  two  arms  i,  which  pass  round  the 
plate  across  its  horizontal  diameter. 

Fig.  362. 


Fig.  364. 


Figs.  363  and  364  exhibit  more  plainly  the  arrangement  of  the 

cushions,    and   the   manner   in 
which  they  are  secured. 

If  we  turn  the  glass  disc 
round,  by  means  of  the  winch, 
it  will  become  positively  electric 
by  the  friction  against  the  leather 
cushion  covered  with  amalgam. 
After  turning  the  disc  one-quar- 
ter round,  one  spot  on  the  disc 
lying  between  the  cushions  al- 
ways comes  to  the  arms  i.  The 
+  electricity  of  the  glass  acts 
here  decomposingly  upon  the 
conductor;  the  —  electricity  is 


THE   ELECTRIFYING   MACHINE. 


383 


attracted,  and  flows  over  the  glass,  and  then  brings  it  back  to  its 
former  condition,  that  is,  neutralizing  more  or  less  entirely  its  + 
electricity.  This  latter  electricity  remains  upon  the  conductor. 

In  order  to  prevent  the  electricity  of  the  glass  from  being  wasted 
in  the  air,  on  its  passage  from  the  rubber  to  the  arm  i,  the  disc  is 
protected  on  both  sides  by  pieces  of  oil-silk.  It  is  necessary  to 
rub  the  glass  legs  and  the  disc  with  warm  woolen  cloths,  or  with 
heated  dry  blotting-paper,  before  using  the  apparatus,  in  order  that 
it  may  work  efficiently. 

The  —  electricity  of  the  rubber  passes  to  the  ground,  and  its 
escape  is  necessary,  since,  if  it  were  to  remain  upon  the  cushion, 
it  would  acquire  such  a  degree  of  tension  as  partially  to  flow  over 
the  glass  plate,  and  partially  neutralize  the  -f  electricity.  The 
electricities  that  are  liberated  by  friction  must  immediately  be 
carried  off  at  the  spot  where  they  are  set  free,  otherwise  we  should 
be  unable  to  develop  electricity  again  at  the  same  place. 

Glass  cylinders  are  used  as  well  as  the  plates  in  the  construction 
of  electrifying  machines.  Fig.  365  represents  a  cylinder-machine, 

Fig.  365. 


which,  as  usual,  is  so  arranged  that  positive  and  negative  elec- 
tricity may  be  engendered  at  will ;  a  is  the  glass  cylinder  revolving 
upon  a  horizontal  axis  6,  and  rubbed  throughout  its  whole  length 
by  a  single  cushion  e.  This  cushion  is  connected  with  a  con- 
ductor r.  The  conductor  v  is  diametrically  opposite  to  the  cushion 


384  THE    STEAM    ELECTRIFYING   MACHINE. 

e,  and  is  provided  with  points  on  the  side  turned  towards  the 
cylinder.  The  upper  half  of  the  cylinder  is  protected  by  a  piece 
of  oil  silk  fastened  to  the  rubber  e,  so  that  the  glass  rubbed  at  e 
may  not  lose  its  electricity  on  its  passage  to  the  conductor  v.  The 
latter  is  of  course  charged  with  +  electricity.  If  we  wish  for  a 
powerful  charge  of  -f-  electricity  on  v,  we  must  put  the  conductor 
r  in  connection  with  the  ground.  On  the  other  hand,  we  must 
take  care  to  enable  the  -f  electricity  to  pass  freely  from  the  con- 
ductor v,  if  we  want  to  have  a  strong  charge  of  —  electricity  on 
the  conductor  r. 

The  Steam  Electrifying  Machine. — Many  years  ago,  the  dis- 
covery was  accidentally  made,  in  England,  that  a  boiler,  from 
which  steam  was  forcibly  propelled  through  a  small  aperture,  was 
strongly  electric ;  by  pursuing  this  discovery,  means  were  found 
for  converting  a  steam  boiler  into  an  electrifying  machine  far  sur- 
passing, in  its  action,  every  known  apparatus  of  the  kind.  Fig. 
366  represents  a  machine  of  this  description  of  medium  size. 
The  boiler,  which  is  18  inches  in  diameter,  and  3  feet  in  length, 
rests  upon  four  glass  legs.  It  is  heated  internally  in  a  similar 
manner  as  the  boilers  used  in  steamboats.  Fig.  367  is  a  section 
of  the  boiler. 

On  the  top  of  the  boiler  there  is  a  cap,  to  which  a  short  brass 
tube,  closeable,  by  means  of  a  cock,  is  attached ;  the  conducting 
pipes  may  be  screwed  on  the  short  tube,  and  will  presently  be 
described. 

Before  the  cap  there  is  a  safety  valve,  whose  weight  is  mova- 
ble, and  may  so  far  project  that  the  steam  must  exert  a  pressure 
of  90  Ibs.  on  the  square  inch,  before  it  can  raise  the  valve. 

On  the  reverse  side  of  the  boiler  there  is  a  glass  tube  con- 
nected above  and  below  with  the  boiler,  so  that  we  may,  by  this 
tube,  see,  as  in  locomotives,  the  height  at  which  the  water 
stands. 

Fig.  368  represents  the  apparatus  with  its  conducting  aper- 
tures delineated,  as  seen  from  above.  The  cast  iron  tube  b  c 
(Fig.  366),  about  8  inches  in  length,  and  2  inches  in  diameter,  is 
screwed  on  at  a.  From  this  tube  the  steam  escapes  through  6 
horizontal  tubes  d  df,  which  pass  through  a  box  of  brass-plate 
filled  with  cold  water,  by  which  means,  a  portion  of  the  escaping 
steam  is  condensed,  and  the  action  considerably  increased. 

At  an  opening  o  in  the  upper  cover  of  the  box  F,  a  brass  tube 


THE    STEAM    ELECTRIFYING   MACHINE. 


385 


is  put  on,  which  passes  at  n  (Fig.  366)  into  the  chimney,  and 
gives  a  passage  to  the  steam  formed  in  the  box  F. 


Fig.  366. 


Fig.  367. 


Fig.  369. 


Fig.  369  gives  a  section  of  the  conducting  pipes  dr  represented 
in  Fig.  368,  at  about  half  their  actual  size.  At 
the  end  of  the  tube,  a  piece  of  brass  M  N  is 
screwed  on,  having  a  wooden  plug  a  b  c  d,  which 
forms  the  end  of  the  escape  aperture.  This 
longitudinally  bored  wooden  cylinder  is  secured 
to  its  place  by  a  short  brass  cylinder  r  screwed 
into  the  brass  work  M  N.  A  brass  plate  is  so 
placed  before  the  opening  of  the  bored  cylinder 
r,  that  the  steam  must  pass  along  the  winding  course,  designated 
by  the  arrow,  before  it  can  escape  by  the  opening. 

If  the  apparatus,  in  Fig.  368,  be  screwed  on  the  boiler,  and 
the  steam  have  the  necessary  force  of  tension,  the  separating 
33 


386  THE    STEAM    ELECTRIFYING    MACHINE. 

cock  will  be  opened  by  turning  the  handle  t,  Fig.  366,  a  quarter 
round,  and  the  steam  escaping,  with  force,  from  the  six  openings, 
the  boiler  will  become  electric.  The  escaping  steam  has  the 
opposite  electricity  to  that  contained  in  the  boiler ;  in  order  to 
heighten  the  action  of  the  apparatus,  it  is  essential  to  let  the 
steam  escape  as  fast  as  possible,  and  this  is  best  effected  by 
placing,  in  the  current  of  steam,  a  row  of  metallic  points  fastened 
to  a  brass  rod  communicating  with  the  ground.  This  rod,  or  staff, 
stands  on  a  glass  pedestal,  by  which  it  may  be  insulated  to  prove 
that  the  steam  has  really  the  opposite  kind  of  electricity  to  that  of 
the  boiler. 

By  means  of  this  hydro-electrifying  machine,  a  battery  of  36 
square  feet,  in  area,  may  be  perfectly  charged  in  the  space  of  30 
seconds. 

The  source  of  this  strong  development  of  electricity  is  not 
owing  to  the  formation  of  gas,  as  we  might,  at  first,  be  inclined 
to  believe ;  but  entirely  to  the  friction  against  the  sides  of  the  tube 
of  the  violently  escaping  steam  that  is  mixed  with  particles  of 
water.  That  such  is  really  the  case,  is  proved  by  the  escape  of 
the  electricity  every  moment  the  safety-valve  is  opened,  although 
the  formation  of  steam  continues,  in  the  meantime,  uninterrupted. 

For  the  generation  of  electricity,  it  is  essential  that  the  already 
condensed  particles  of  water  should  be  carried  away  with  the 
escaping  steam  through  the  apertures,  an  object  which  is  effected 
by  the  condensation  apparatus  JF,  seen  in  Fig.  368.  If  the  escape 
pipes  be  of  sufficient  length,  we  may  dispense  with  a  special  cool- 
ing apparatus. 

When  the  opening  for  the  steam  is  formed  by  a  wooden  tube, 
as  delineated,  the  boiler  will  be  in  a  state  of —  electricity,  and  the 
steam  in  one  of  4-  electricity ;  the  same  is  the  case  when  metal 
or  glass  is  used  for  the  purpose ;  and,  if  an  ivory  tube  be  used,  the 
boiler  will  scarcely  manifest  a  trace  of  a  charge.  On  applying  a 
little  oil  of  turpentine  to  the  mouth  of  the  tube,  the  boiler  will  be 
positively,  and  the  steam  negatively  electric. 


OF    ELECTRIC    FORCES.  387 


CHAPTER  III. 

OF    ELECTRIC     FORCES. 

Diminution  of  Electrical  Power  with  the  Increase  of  Distance. 
— The  law  by  which  electrical  attractions  and  repulsions  diminish 
in  proportion  as  the  distance  increases,  may  be  shown  by  the  os- 
cillations of  an  electric  pendulum.  We  must  let  a  small  shell-lac 
needle,  horizontally  suspended  by  a  silk  thread,  and  supporting  at 
one  end  a  disc  of  electrified  gold  leaf,  oscillate  by  the  influence  of 
an  electrified  insulated  ball.  If  the  ball  and  the  disc  be  charged 
with  the  same  electricity,  the  disc  will  form  the  end  of  the  elec- 
trified pendulum  turned  away  from  the  ball ;  but  if  the  electricities 
of  the  disc  and  the  ball  be  different,  the  former  will  be  turned 
towards  the  latter.  We  may,  in  like  manner,  judge  of  the  accele- 
rating force  exercised  on  the  electric  pendulum  by  its  oscillations. 
From  these  data  it  may  be  seen  that  electrical  attractions  and 
repulsions  stand  in  an  inverse  relation  to  the  squares  of  distance. 

Distribution  of  Electricity  on  the  Surfaces  of  Conducting  Bodies. 
— As  long  as  a  body  remains  in  a  natural  condition,  that  is,  as  long 
as  the  two  electric  fluids  are  not  combined,  they  are,  probably, 
uniformly  distributed  through  the  whole  mass  of  the  body.  As 
soon,  however,  as  one  fluid  becomes  separated  from  the  other,  and 
a  conductor  is  charged  with  free  electricity,  the  individual  elements 
of  these  freed  electricities  will  act  repulsively  upon  each  other, 
retreating  as  far  apart  as  possible,  until  checked  by  some  impe- 
diment. A  perfectly  good  conducting  body  cannot  oppose  any 
resistance  within  itself  to  this  dispersion  ;  the  electricity,  there- 
fore, distributes  itself  over  its  surface,  and  would  be  still  further 
dispersed  if  the  body  were  in  a  space  easily  penetrated  by  the  elec- 
itricity.  Electricity  always  distributes  itself  over  the  surface  of  a 
conductor,  on  which  it  is  retained  by  the  atmosphere,  which  en- 
velops it  as  if  it  were  a  non-conducting  layer. 

The  following  experiment  will  show,  in  the  simplest  manner, 
that  electricity  only  distributes  itself  over  the  surface,  and  not 
through  the  interior  of  bodies. 

A  ball,  7  or  8  inches  in  diameter,  and  having  a  hollow  8  or  10 


388  DISTRIBUTION    OF    ELECTRICITY    ON    THE 

lines  in  breadth,  and  1  inch  in  depth,  must  be  insulated  and 
charged  with  electricity ;  if,  now,  we  touch  this  ball  in  any  part, 
with  a  test  disc,  it  will  become  charged  with  electricity,  while,  on 
touching  the  bottom  of  the  hollow,  with  the  test  disc,  it  will  not  be 
removed  from  its  natural  condition.  Let  us  now  consider  the 
manner  in  which  electricity  distributes  itself  over  the  surface  of 
bodies. 

If  we  electrify  an  insulated  body,  the  law  of  symmetry  requires 
that  the  electricity  should  distribute  itself  uniformly  over  the 
whole  surface,  forming  everywhere  a  layer  of  equal  density.  We 
may  convince  ourselves  by  experiment  that  such  is  the  case.  If, 
for  instance,  we  touch  the  electrified  ball  at  any  spot  with  the 
test  disc,  the  latter  will  immediately  form,  as  it  were,  an  element 
of  the  spherical  surface,  as  large  a  quantity  of  electricity  distri- 
buting itself  over  its  surface  as  there  was  upon  the  portion  01 
the  sphere  covered  by  the  disc  ;  the  strength  of  the  electric  charge 
in  the  disc  may  be  determined  after  its  removal  from  the  sphere, 
by  bringing  it  into  contact  with  the  plate  of  an  electroscope.  The 
divergency  of  the  pieces  of  gold  leaf  will  be  the  same,  at  whatever 
part  of  the  ball  we  attach  the  disc. 

If  the  insulated  conductor  to  be  electrified  be  not  spherical,  no 
equal  distribution  of  the  electricity  will  take  place,  that  is  to  say, 
the  electrical  layer  distributed  over  the  body  will  not  be  every- 
where equally  dense.  If,  by  the  aid  of  a  test  disc,  we  test  the 
density  of  the  electricity  at  different  parts  of  a  cylinder,  with 
rounded  ends,  (Fig.  370,)  we  shall  find  the  density  of  the  electri- 
Fi  370  city,  greater  at  the  extremities  than  in  the  mid- 

dle. The  disc  will  be  much  more  strongly 
charged,  on  holding  it  to  the  end  of  the  cylin- 
der, in  such  a  manner  that  its  edge  shall  not 
touch  the  top  of  it,  but  that  its  plane  shall  lie 
in  the  line  of  prolongation  of  the  axis  of  the  cylinder.  Similar 
results  are  obtained  by  examining  the  electrical  condition  of  a 
disc,  for  instance,  the  cover  of  an  electrophorus.  We  may  easily 
understand  that  a  distribution  of  electricity  must  occur  on  the  sur- 
face of  bodies  possessing  unequal  expansion  in  different  directions, 
for,  in  consequence  of  the  mutual  repulsion  of  the  separate  parti- 
cles of  the  electric  fluid,  these  particles  will  retire  as  far  as 
possible  from  the  middle  of  the  body,  accumulating  in  its  remotest 
projections. 


SURFACES  OF  CONDUCTING  BODIES. 

The  more  a  body  departs  from  the  spherical  form,  the  less 
equally  is  electricity  distributed  over  its  surface,  and  the  more 
does  it  collect  at  the  points  lying  most  remote  from  the  middle, 
and  that,  in  proportion  to  the  want  of  density  in  those  parts.  It 
follows,  therefore,  that  if  a  point  be  brought  near  an  insulated 
conductor,  the  electricity  will  have  an  extraordinary  density  at 
this  pointed  end.  But  the  denser  the  electricity  is  at  any  point, 
the  sooner  will  it  be  able  to  overcome  the  resistance  of  the  air, 
which  strives  to  keep  it  upon  the  body.  Hence  it  happens,  that 
electricity  flows  so  readily  from  sharply  pointed  bodies. 

We  might  adduce  a  number  of  experiments  by  which  this 
power  of  pointed  bodies  is  manifested,  but  we  will  limit  ourselves 
to  a  few  illustrations. 

1.  On  putting  a  point  to  the  end  of  the  conductor  of  an  elec- 
trifying machine,  it  will  be  found  impossible  to  charge  it  in  such 
a  manner  as  to  draw  sparks  from  it.     All  the  electricity  engen- 
dered by  the  turning  of  the  machine  being  immediately  discharged 
by  the  point. 

2.  In  the  same  manner,  on  bringing  a  point  that  is  in  connec- 
tion with  the  ground  within  a  few  inches  of  the  conductor  of  the 
machine,  it  will  be  equally  impossible  to  charge  the  conductor. 
The  electricity  of  the  latter  decomposing  the  combined  electricities 
of  the  point,  and  repelling  the  like  kind,  while  it  will  attract  the 
contrary,  and  this  contrary  electricity  will  accumulate  with  such 
brce  at  the  point  as  to  pass  over  to  the  conductor  and  neutralize 
the  electricity  of  the  latter. 

On  the. above  mentioned  property  of  pointed  bodies  rests  the 
construction  of  lightning  conductors. 

Angles  and  sharp  edges  to  conducting  bodies  act  similarly  to 
joints.  It  is,  therefore,  essential,  carefully  to  avoid  all  angular 
brms  in  the  construction  of  any  apparatus  destined  to  retain  elec- 
tricity. 

On  bringing  an  insulated  electric  conductor  near  another  con- 
ductor, the  distribution  of  the  electricity  on  the  surfaces  will 
experience  considerable  modifications.  If  we  bring  an  electric 
insulated  sphere  near  another  body  of  the  same  kind,  likewise 
insulated  and  charged  with  the  same  electricity,  there  will  no 
longer  be  a  uniform  distribution  of  electricity  upon  the  surface. 
As  the  electricity  of  the  one  sphere  repels  that  of  the  other,  the 
density  of  the  electricity  will  be  the  most  inconsiderable  at  those 

33* 


390 


OF    COMBINED    ELECTRICITY. 


Fig.  371. 


Fig.  372. 


points  of  the  spheres  turned  towards  each  other,  and  greatest  at 
the  most  remotely  opposite  points.  Figs.  371  and  372,  represent 

two  balls.  At  a  and  b  the 
density  of  the  electricity  is 
at  the  minimum,  at  c  and 
d  it  is  at  the  maximum. 
The  nearer  we  bring  the 
two  balls,  the  more  will  the 
density  diminish  at  a  and 
b,  and  increase  at  c  and  a. 
If  we  bring  these  spheres 
into  contact,  the  density  of 
the  electricity  will  be  null 

at  the  point  of  contact.  If  the  two  spheres  had  been  charged  with 
opposite  electricities,  we  should  have  found  the  greatest  density 
at  a  and  6,  and  the  smallest  at  c  and  d.  The  accumulation  of 
electricity  increases  at  a  and  b  on  bringing  the  spheres  near  to- 
gether, until  at  last  a  spark  is  emitted. 

A  non-electric  conductor,  on  being  brought  near  an  electrified 
insulated  conductor,  will  act  similarly  to  a  body  charged  with  the 
opposite  electricity,  as  it  becomes  electric  by  induction  or  approxi- 
mation to  the  conductor. 


CHAPTER    IV. 


OF    COMBINED    ELECTRICITY. 

WE  have  already  seen  that  if  two  insulated  conductors  charged 
with  opposite  electricities  be  separated  by  a  layer  of  air,  the  elec- 
tricity of  the  one  will  attract  that  of  the  other,  in  such  a  manner 
that  we  may  alternately  put  either  body  in  connection  with  the 
ground  without  its  electricity  being  entirely  carried  off.  In  Figs. 
371  and  372,  for  instance,  the  ball  to  the  left  is  charged  with  +, 
and. that  to  the  right  with —  electricity,  and  we  alternately  touch 
either  with  the  finger  without  the  charge  being  lost.  The  elec- 
tricity of  the  one  sphere  is  attracted  by  the  opposite  electricity  of 
the  other  sphere,  and  is  thus  prevented  from  escaping,  being  com- 


OF    COMBINED    ELECTRICITY.  391 

bined.  The  nearer  we  bring  these  two  kinds  of  electricity  to 
each  other,  the  more  strongly  will  they  be  mutually  attracted,  and 
the  more  perfect  will  be  their  combination;  if,  however,  the  two 
conductors  be  separated  only  by  a  layer  of  air,  the  combination 
will  not  be  perfect,  as  we  cannot  bring  them  very  near  each  other 
without  the  layer  of  air  being  broken,  and  a  spark  emitted.  To 
make  the  combination  as  perfect  as  possible,  the  two  conductors 
charged  with  opposite  electricities  must  in  the  place  of  air  be 
separated  by  some  other  insulator  capable  of  opposing  a  greater 
resistance  to  the  passage  of  electricity,  and  for  this  purpose  glass 
or  resin  answers  best. 

The  Franklin  plate  is  especially  well  adapted  to  facilitate  the 
examination  of  the  properties  of  combined  electricity.  Fig.  373 
represents  a  glass  plate,  the  sides  of  which 

are  about  1  foot  in  length.     The  middle  of    Fig^373' 

the  glass  on  either  side  is  covered  with 
tin  foil,  leaving  a  free  margin  all  round  of 
about  a  hand's  breadth.  We  may  varnish 
over  the  uncovered  parts  of  the  glass,  in 
order  the  better  to  insulate  them.  If  we 
charge  the  front  part,  covered  with  the  tin 
foil,  with  -f,  and  the  reverse  side  with  — 
electricity,  the  opposite  electricities  will  be 
separated  from  each  other  merely  by  the 
thickness  of  the  glass  disc ;  this  they  are, 
however,  unable  to  penetrate,  and  thus  the 
combination  will  be  tolerably  well  effected. 

To  charge  the  two-coated  sides  of  the  Franklin  plate  with  op- 
posite electricities,  it  is  unnecessary  to  bring  each  into  connec- 
tion with  the  source  of  electricity.  If  we  bring  one  side,  (the 
front  one,)  into  communication  with  the  conductor  of  the  electri- 
fying machine,  a  portion  of  the  +  electricity  will  pass  off  from 
the  conductor  to  the  coated  surface.  The  electricity  of  the  front 
surface  acts  inductively  upon  the  combined  electricities  of  the 
back  surface ;  and  as  soon  as  we  place  it  in  communication  with 
the  ground,  the  +  electricity  will  pass  into  the  ground,  while  the 
-  electricity  will  be  induced  to  the  reverse  surface.  But  the  — 
electricity  of  the  reverse  side  acts  repulsively  upon  the  -f  electri- 
city of  the  front  side,  thus  enabling  electricity  to  pass  again  from 
the  conductor  to  the  front  coated  surface,  which  again,  by  its  re- 


392 


OF    COMBINED    ELECTRICITY. 


pulsive  power,  increases  the  —  electricity  of  the  reverse  side. 
We  may  in  this  manner  easily  charge  one  coated  surface  with  -f , 
and  the  other  with  —  electricity. 

However  small  the  distance  separating  the  two  surfaces,  the 
mutual  combination  is  not  perfect.  In  order  to  have  the  elec- 
tricity perfectly  combined  on  the  one  side,  it  is  necessary  that 
there  should  be  an  excess  of  electricity  on  the  other,  that  is,  that 
free  electricity  must  be  present.  On  touching  the  one  coated 
surface  of  a  charged  Franklin  plate  with  the  finger,  while  the 
other  side,  (the  front  for  instance,)  is  no  longer  in  connection  with 
the  conductor,  we  can  only  bring  off  a  portion  of  electricity,  while 
a  strong  charge  of  —  electricity  perfectly  combined,  remains  upon 
the  reverse  surface.  In  order,  however,  to  have  this  —  electricity 
perfectly  combined,  it  is  indispensably  necessary  that  there  should 
be  an  excess  of  +  electricity  on  the  opposite  side.  We  may  easily 
convince  ourselves  that  such  is  the  case.  If  after  all  the  non- 
combined  —  electricity  of  the  reverse  side  has  been  carried  off,  we 
touch  the  front  coated  surface,  a  faint  spark  will  be  emitted  on  the 
approximation  of  the  finger,  which  proves  that  free  electricity  is 
present.  If  now  we  remove  all  the  free  +  electricity  from  the 
front  side,  there  will  again  be  free  —  electricity  on  the  opposite 
side,  and  we  may  draw  a  faint  spark  from  the  reverse  coated  sur- 
face, &c. 

The  excess  of  electricity  which  must  be  present  on  the  one 
surface,  in  order  perfectly  to  combine  the  opposite  electricity  on 
the  other  side,  may  be  made  apparent  to  the  eye. 
We  must  secure  with  wax,  a  light  electric  pendu- 
lum on  each  side  of  the  disc  in  the  manner  re- 
presented in  Fig.  374,  which  shows  a  diagonal 
section  of  the  disc.  On  the  side  on  which  there 
is  free  electricity,  the  pendulum  will  be  repelled, 
while,  on  the  other  side  it  will  remain  hanging 
vertically,  and  in  contact  with  the  coated  surface. 
If  we  touch  the  pendulum  on  the  one  side  where 
there  is  free  electricity,  the  pendulum  will  fall, 
while  the  one  on  the  opposite  side  will  rise.  We 
may,  therefore,  by  alternately  touching  one  or 
other  of  the  sides,  make  either  pendulum  rise. 

This  phenomenon  may  be  easily  explained. 
If  there  be  an  excess  of  +  electricity  on  the  one  side,  it  will  act 


Fig.  374. 


OF    COMBINED    ELECTRICITY. 


393 


attractively  upon  the  electricity  on  the  other  surface,  as  well  as 
upon  the  little  electricity  in  the  ball  of  the  pendulum.  The  — 
electricity  certainly  repels  the  —  electricity  in  the  ball,  but  the 
force  with  which  the  excess  of  -f  electricity  attracts  the  negative 
ball  is  greater  than  the  force  of  repulsion.  On  carrying  off  the 
excess  of  -f  electricity,  the  liberated  —  electricity  distributes 
itself  partially  over  the  ball  which  is  now  repelled,  there  being 
no  excess  of  +  electricity  present  on  the  other  side  to  hold  it 
back. 

The  .apparatus  will,  by  degrees,  become  wholly  discharged  if 
we  continue  alternately  to  touch  the  two  surfaces  with  the  finger, 
and  thus  remove  all  the  free  electricity  on  the  one  side.  If  we 
touch  both  surfaces  at  once,  or,  by  any  other  means,  put  them 
into  connection  with  each  other,  the  discharge  will  take  place  all 
at  once,  while  the  accumulated  opposite  electricities  of  the  two 
surfaces  will  pass,  in  this  manner,  from  one  to  the  other.  The 
discharging  rod,  represented  in  Fig.  375,  is 
commonly  used  for  this  purpose.  It  consists  of 
two  curved  brass  rods  b  c  and  b'  c,  which  are 
united  at  c  by  a  hinge.  Each  arm  of  the  dis- 
charging rod  terminates  in  a  small  brass  ball 
b  and  &',  and  is  also  provided  with  an  insulated 
handle  m  and  m'.  We  must  touch  one  surface 
with  one  of  the  balls,  and  on  approximating  the  other  to  the  op- 
posite, a  spark  of  vivid  light  will  be  emitted,  at  a  certain  distance, 
with  loud  explosion. 

The  Leyden  jar  is,  in  principle,  nothing  but  a  modification  of 
Franklin's  plate,  and  consists  of  a 
glass  vessel,  covered  externally  with 
tin  foil  to  within  a  few  inches  of  the 
rim ;  internally,  the  vessel  is  simi- 
larly coated,  or  filled  with  some  con- 
ducting substance,  as  iron  filings  or 
small  seed.  The  inner  coating  is 
connected  with  a  brass  rod  passing 
through  the  stopper  or  cover  of  the 
vessel,  and  ending  in  a  knob.  Figs. 
376  and  377  represent  two  forms 

of  the  Leyden  jar.  The  part  of  the  glass  that  is  not  covered 
must  be  varnished.  To  charge  the  jar,  the  external  coating  must 


Fig.  376. 


394  THE    LEYDEN   JAR. 

be  brought  into  connection  with  the  ground,  and  the  knob  with 
the  conductor  of  the  machine.  We  may,  however,  reversely, 
put  the  inner  coating  into  connection  with  the  ground,  and  con- 
nect the  external  one  with  the  conductor  of  the  machine.  Leyden 
jars  often  discharge  themselves  when  either  a  spark  is  emitted 
from  the  external  coating  to  the  metal  rod,  or  the  glass  is  broken. 
In  the  latter  case,  the  jar  becomes,  of  course,  unfit  for  further 
use.  When  we  use  several  conducting  bodies,  to  discharge  a 
jar,  the  electricity  will  immediately  pass  over  to  the  best  con- 
ductor. If  we  press  a  metal  wire,  with  one  hand,  to  the  external 
coating,  we  may,  with  impunity,  hold  the  opposite  end  of  the 
wire  to  the  knob,  with  the  other  hand,  the  electric  shock  passing 
through  the  wire,  and  not  the  body ;  to  effect  this,  the  wire  must 
not,  however,  be  very  thin. 

In  order  to  obtain  a  very  strong  charge,  it  is  necessary  to  use 
very  large  jars,  either  separate  or  connected  in  one  electric  bat- 
tery. Fig.  378  represents  an  apparatus  of  this  kind.  All  the 

external  coatings  of  the  jars 
are  in  connection  with  each 
other,  as  well  as  the  inner 
coatings. 

When  the  electric  shock 
passes  from  a  Leyden  jar 
through  the  human  body,  it 
produces  a  sensation  which 
it  would  be  difficult  to  de- 
scribe, an  involuntary  con- 
vulsion of  the  nerves.  The 
best  manner  of  trying  the 

experiment  upon  oneself,  is  to  lay  one  hand  upon  the  external 
coating,  and,  with  the  other,  grasp  the  knob.  In  a  weak  dis- 
charge, the  shock  is  only  perceptible  in  the  fore  part  of  the  arm, 
if  it  be  stronger,  we  then  feel  it  in  the  upper  arm,  producing  an 
even,  sharp  pain  in  the  breast,  and  very  strong  shocks  may  prove 
dangerous.  Powerful  batteries  are  not  necessary  if  we  want  to 
kill  smaller  animals,  as  birds,  hares,  &c.,  by  an  electric  shock; 
the  larger  batteries  are  capable  of  destroying  the  larger  animals. 
Anatomical  examinations  of  the  bodies  of  the  animals,  killed  by 
an  electric  shock,  have  shown  that  there  is  no  injury  inflicted  on 
the  organs;  the  violent  contortions  exhibited,  however,  in  the 


THE   LEYDEN   JAR.  395 

bodies,  where  the  shock  has  not  been  sufficiently  strong  to  pro- 
duce death,  manifest  the  degree  to  which  the  nervous  system  has 
been  affected. 

If  several  persons  form  a  chain  by  holding  each  other's  hands, 
all  will  simultaneously  feel  the  shock,  on  the  one  first  in  the  ring, 
touching  the  external  coating  of  the  jar,  and  the  last  the  knob. 

We  may  ignite  combustible  fluids  much  more  securely  by  aid 
of  a  Leyden  jar  than  by  a  spark  direct  from  the  conductor  of  the 
machine.  Even  pulverized  Colophony,  scattered  over  cotton  wool, 
and  gunpowder  may  be  ignited  by  the  sparks  of  a  discharge  of  a 
Leyden  jar. 

Henley's  general  discharging  rod,  represented  in  Fig.  379,  is 

Fig.  379. 


very  convenient  in  many  experiments  which  may  be  made  with 
the  Leyden  jars  and  the  electric  battery.  The  one  arm  is  in  con- 
nection with  the  external  coating  by  means  of  the  chain  c,  while, 
to  the  other  arm,  is  secured  another  chain  </,  terminating  in  the 
insulated  ball  6.  If  we  want  the  spark  to  pass  through,  we  must 
take  hold  of  the  insulated  handle  of  the  ball  6,  and  bring  it  quickly 
to  the  knob  of  the  bottle.  The  spark  will  strike  at  6,  between  the 
two  balls  d  and/1,  lying  on  an  insulated  plane. 

If  the  balls  d  and  /  be  united  by  a  very  thin  iron  wire,  the 
latter  will  be  heated  on  letting  a  faint  charge  pass  through  it, 
while  a  stronger  charge  will  make  it  red  hot,  and  one  still  stronger 
than  the  former  will  cause  it  to  fly  asunder  in  separate  melted 
globules,  which  will  be  thrown  to  a  great  distance. 

Bad  conductors,  that  interrupt  the  course  of  the  discharge,  are 


396  THE    CONDENSER. 

broken  in  fragments,  or  filled  with  holes,  if  the  accumulation  of 
the  electricity  be  sufficiently  considerable.  A  wooden  disc,  for 
instance,  from  3  to  4  inches  in  diameter,  and  from  3  to  5  lines  in 
thickness,  is  penetrated  by  the  discharge.  The  same  thing  occurs 
with  respect  to  one  or  more  cards,  pasteboard  covers,  &c.  To 
make  this  experiment,  we  must  place  the  bodies  we  wish  to  pe- 
netrate between  the  balls  of  Henley^s  discharging  rod  in  such  a 
manner  that  the  latter  may  be  in  contact  with  the  intervening 
bodies. 

The  Condenser. — Properly  speaking,  every  apparatus  in  which 
combined  electricity  is  accumulated  is  a  condenser ;  consequently, 
the  Franklin  plate,  and  the  Leyden  jars,  may  be  considered  as 
Fig.  380.  condensers.     The  term,  however,  is 

generally  limited  to  those  apparatus 
that  serve  to  make  electricity,  pos- 
sessing a  feeble  tension,  perceptible 
by  condensation.  Condensers  con- 
sist especially  of  two  conducting 
plates,  separated  by  a  non-conduct- 
ing medium.  Passing  by  the  less 
perfect  instruments  of  this  kind,  we 
will  here  only  speak  of  the  con- 
denser used  in  combination  with  the 
gold-leaf  electrometer.  On  this  last 
named  instrument,  we  screw  a  metal 
plate,  as  seen  in  Fig.  380.  The 
plate  must  be  smoothly  cut,  and  co- 
vered on  its  upper  surface  with  a 
very  thin  layer  of  varnish,  composed 
of  a  solution  of  shell-lac  in  spirits  of 
wine,  put  on  lightly  with  a  brush  while  in  a  very  fluid  state,  on 
which  it  will  rapidly  dry.  We  now  take  a  second  plate,  similarly 
prepared  and  provided  with  an  insulated  handle,  and  place  its 
varnished  surface  upon  the  other  plate,  in  such  a  manner  that  the 
metal  plates  are  merely  separated  by  the  thin  layer  of  varnish, 
otherwise  fitting  together  as  exactly  as  possible.  This  arrange- 
ment 'corresponds  perfectly  with  the  Franklin  plate,  the  glass  plate 
being  replaced  by  the  thin  shell-lac  layer,  and  the  plates  serving 
as  a  substitute  for  the  tin-foil  coatings,  the  only  difference  being, 
that,  in  this  apparatus,  we  may  lift  off  the  upper  plate  at  will, 


ELECTRIC    LIGHT.  397 

while  the  two  coatings  in  the  Franklin  plate  are  immovable.  As 
the  insulating  layer  is  so  very  thin,  and  the  plates,  consequently, 
so  close  together,  a  perfect  combination  may  be  effected.  If  we 
bring  the  lower  condensing  plate  into  connection  with  a  weak 
source  of  electricity,  touching  the  upper  plate  with  the  finger  to 
discharge  it,  the  condenser  will  be  charged  in  a  similar  manner 
to  the  Leyden  jar,  the  external  coating  of  which  is  not  insulated, 
while  the  inner  one  is  in  connection  with  the  conductor  of  the 
machine. 

The  whole  difference  rests  in  this,  that  at  one  time  we  have  a 
large  source  of  electricity,  at  another,  one  of  small  electric  ten- 
sion ;  in  both  cases,  however,  a  condensation  of  electricity  occurs 
in  a  similar  way. 

When  the  condenser  is  charged,  the  upper  plate  must  be  raised, 
(and  that  as  vertically  as  possible,  so  that  the  contact  between  the 
two  plates  may  be  destroyed  at  the  same  moment  at  all  points  ;) 
by  this,  the  hitherto  combined  electricity  of  the  under  plate  will 
be  liberated,  passing  down  into  the  gold  leaf  plates,  and  causing 
them  to  diverge.  When  we  come  to  speak  of  galvanism,  we  shall 
become  acquainted  with  numerous  modes  of  applying  the  con- 
denser. 


CHAPTER    V. 

ELECTRIC  LIGHT  AND   THE  MOTIONS  OF  ELECTRIFIED  BODIES. 

THE  strongest  electric  discharges  that  can  be  accumulated  in 
a  body  will  never  afford  the  least  appearance  of  light  as  long  as 
a  state  of  electric  equilibrium  subsists,  and  the  electric  fluids  are 
at  rest.  The  first  requisite  for  the  appearance  of  electric  light  is, 
therefore,  the  motion  of  the  fluids,  and  a  disturbance  of  the  equi- 
librium. This  condition  is  always  indispensable,  but  by  no  means 
sufficient,  it  being  necessary,  besides,  that  the  tension  affecting  the 
electric  discharge,  should  be  adequately  great.  Whilst,  for  in- 
:stance,  the  electricity  of  a  less  powerful  machine  can  pass  through 
a  metal  wire  into  the  ground,  without  any  light  being  visible  in 


O/l 


398  ELECTRIC    LIGHT. 

the  dark,  we  may  see  the  wire  of  a  strongly  charged  machine  sur- 
rounded by  a  luminous  brightness.  The  tension  necessary  to 
produce  electric  light  depends  upon  the  condition,  form  and  con- 
ductibility  of  the  medium  through  which  the  electricity  must  pass. 
Weak  tension  will  often  afford  a  bright  light,  while,  in  other  cases, 
the  strongest  tensions  are  insufficient  to  give  the  least  manifesta- 
tion of  light. 

Electric  Light  in  the  Mr^  and  in  other  Gases  under  the  Pressure 
of  the  Atmosphere. — The  distance  at  which  a  spark  can  be  drawn 
from  an  electric  body,  depends  upon  the  conductibility  of  the 
substance,  the  size  of  the  surface,  and  the  power  of  the  electric 
charge.  Electricity  flows  spontaneously  from  angular  bodies  and 
points  even  under  very  weak  tension,  and  we  may  in  the  dark 
observe  glittering  brushes  of  light,  several  inches  in  length.  A 
very  strong  charge  is  necessary  to  make  round  bodies  emit  sparks 
spontaneously ;  if,  however,  we  bring  them  near  a  conductor  con- 
nected with  the  earth,  sparks  will  be  emitted,  under  some  circum- 
stances, to  a  great  distance,  forming  a  zigzag  line  like  the  course 
of  lightning. 

In  order  to  multiply  the  sparks,  it  is  necessary  to  interrupt  the 
conductor  by  which  the  electricity  passes  to  the  earth,  and  by  this 
means  many  striking  effects  will  be  produced. 

We  may,  by  means  of  metal  beads  (strung  upon  a  silk  thread, 
but  separated  some  millimetres  from  each  other  by  knots),  form 
ciphers  and  figures  of  various  kinds,  which  will  continue  to  shine 
as  long  as  we  turn  the  machine,  from  whose  conductor,  electricity 
passes  through  the  chain  into  the  ground. 

Lightning   conductors  are  glass  tubes,  on  which  rhomboidal- 

shaped  plates,  covered  with  tinfoil,  are  placed  in  the  order  repre- 

Fi    3gl  sented  in  Fig.  381.  They  are  generally  laid 

on  in  such  a  manner  as  to  pass  round  the 

tube   like   a   progressive   screw  line.     If, 

while  we  are  holding  the  one  end  of  such  a  tube  in  the  hand,  we 

bring  the  other  near  the  conductor,  as  the  machine  revolves,  we 

shall  in  the  dark  see  sparks  continuously  pass  between  every 

two  plates,  so  as  to  appear  like  one  connected  line  of  light  upon 

the  tube. 

A  lightning  plate  is  represented  in  Fig.  382.  A  row  of  stripes 
covered  with  tinfoil  is  glued  upon  a  glass  plate,  as  shown  in 
the  figure,  so  that  a  metallic  line  of  connection  goes  from  a  to 


ELECTRIC   LIGHT   IN   RAREFIED   AIR. 


399 


Fig.  382. 


Fig.  383. 


z,  provided  it  is  not  interrupted  at  the  spots  marked  with  small 
crosses.  If  we  bring  z  into  connection  with 
the  external  coating  of  a  Leyden  jar,  and 
then  establish  a  connection  between  a  and 
the  knob  of  the  jar,  sparks  will  be  evolved 
at  the  places  where  the  connecting  line  is 
interrupted.  We  may,  in  this  manner,  re- 
present ciphers,  and  all  kinds  of  figures. 

These  devices  may  be  altered  in  a  great 
many  different  ways  ;  the  preceding  exam- 
ples must,  however,  suffice. 

The  brush  of  light  observed  in  the  dark, 
on  placing  upon  the  conductor  of  the  elec- 
trifying machine  a  point  from  which  the 
electricity  may  flow,  is  represented  in  Fig.  383.     Negative  elec- 
tricity  never   gives    such   divergent    and  large 
brushes  of  light  as  the  positive.    This  remarkable 
phenomenon  is  very  deserving  of  attention,  as  it 
appears  to  afford  a  characteristic  difference  by 
which  we  may  define  the  two  electric  fluids. 

On  bringing  a  metal  point  near  the  conductor 
of  a  machine  with  the  hand,  we  observe  this  brush 
of  light. 

The  electric  spark  of  the  machine  is  very  bright  in  condensed 
atmospheric  air,  white  and  intense  in  carbonic  acid  gas,  red  and 
faint  in  hydrogen,  yellow  in  steam,  and  of  an  apple- green  color 
in  ether  and  alcohol. 

The  phenomena  of  light  evolved  from  the  electricity  of  a  ma- 
ichine  are  a  true,  although  faint  image,  of  the  electric  atmospherical 
'phenomena  exhibited  in  thunder-storms. 

Electric  Light  in  Rarefied  Air. — If  a  glass  tube,  several  feet  in 
j.ength,  and  provided  at  both  extremities  with  metal  caps,  be  ex- 
lausted,  and  the  one  end  be  connected  with  the  conductor  of  the 
inachine,  and  the  other  end  with  the  ground,  we  shall  see  a  vivid 
ight  within  the  tube.  As  the  electricity  in  the  rarefied  air  meets 
with  only  a  weak  resistance,  it  extends  throughout  the  whole  tube, 
narking  its  passage  by  flashes  of  light.  If  the  connection  be 
sufficiently  maintained,  the  light  will  appear  fixed  and  of  uniform 
•utline,  but  as  soon  as  a  /conducting  body  is  brought  towards  it 


400 


MOTIONS    PRODUCED   BY   THE 


Fig.  384. 


Fig.  385. 


from  without,  it  will  be  drawn  towards  it,  and  will  at  the  same 
time  become  brighter. 

We  generally  take  tubes  several  inches  in  thickness  for  these 
experiments.  A  somewhat  differently  formed  apparatus  is,  how- 
ever, represented  in  Fig.  384,  this  being  an  elliptically-shaped 

glass  vessel.  At  the  two  ex- 
tremities are  metal  fastenings, 
one  of  which  has  a  cock,  which 
may  be  screwed  on  to  an  air- 
pump.  The  fastening,  or  cap, 
on  the  other  side,  is  provided 
with  a  leather  box,  through  which  passes  the  metal  wire  termi- 
nating in  the  knob  &',  which  may  thus  at  will  be  pushed  nearer  to 
6.  When  the  air  has  been  quite  exhausted  from  the  apparatus, 
the  electricity  can  easily  pass,  and  fill  the  whole  vessel  with  light. 
If  a  little  air  be  suffered  to  enter  through  the  cock, 
the  light  will  be  less  diffuse,  forming  purplish  arcs 
of  light  between  b  and  b'.  The  more  air  we  admit, 
the  more  the  expansion  of  these  appearances  of 
light  will  diminish,  approaching  more  and  more  to 
the  form  of  the  ordinary  electric  spark. 

Electricity  likewise  exhibits  phenomena  of  light 
in  the  Toricellian  vacuum. 

Picard  first  remarked,  on  making  the  mercury 
oscillate  up  and  down,  that  a  barometer  was  lumi- 
nous in  the  dark,  and  he  was  soon  convinced  that 
this  phenomenon  depended  upon  the  electricity 
developed  by  the  friction  of  the  mercury  on  the 
sides  of  the  tube.  Cavendish  constructed  the  dou- 
ble barometer,  Fig.  385,  to  observe  electric  light  in  the  Toricel- 
lian vacuum ;  its  application  will  be  understood  without  further 
explanation. 

Motions  produced  by  the  Discharge  of  Electricity. — As  the  phe- 
nomena of  attraction  and  repulsion  have  already  been  described, 
it  only  remains  for  us  to  make  a  few  remarks  upon  the  motions 
occasioned  by  electricity.     A  metal  rod  t  tf,  curved  at  both  ex- 
tremities, in  opposite  directions,  is  placed  on  a  conducting  poin  < 
c p,  Fig.  386,  in  connection  with  the  conductor  of  the  machine!' 
but  in  such  a  manner  that  it  can  easilyplace  itself  in  equilibrium 
although  at  the  same  time  it  can  just  as  easily  turn  in  a  horizontal  j 


DISCHARGE   OF   ELECTRICITY. 


401 


Fig.  387. 


plane  upon  the  point.     Such  an  apparatus  is  termed  an  electric 
fly-wheel.    As  soon  as  the  machine  is  turned,  the     Fi    ^6 
wheel  begins  to  rotate,  and  when  observed  in  the 
dark,  the  electricity  will  be  seen  to  flow  from  the 
points  in  the  forms  of  brushes  of  light. 

This  motion  is  produced  by  the  discharge  of  the 
electric  fluid  from  the  points,  and  corresponds  entirely 
to  the  phenomena  exhibited  by  the  rotation  of  Segner's 
water-wheel. 

Motions  occasioned  by  Electrical  Re-action. — The  legs  of  frogs, 
when  suspended  in  the  vicinity  of  the  conductor  of  an  electrify- 
ing machine,  do  not  appear  to  experience  any  change;  if,  by  the 
turning  of  the  machine,  the  conductor  c  be  charged 
with  positive  electricity,  they  will,  however,  be- 
come electric  by  induction,  the  attracted  —  elec- 
tricity accumulating  at  r,  and  the  repelled  + 
electricity  escaping  into  the  ground  by  the  wire  s. 
As  soon  as  we  draw  a  spark  from  the  conductor 
c,  the  sudden  re-union  of  the  two  electricities 
will  produce  contortions  in  the  frog's  leg,  a  proof 
that  on  a  return  to  its  natural  condition,  the 
molecules  of  the  bodies  are  effected  by  the  pressure  of  the  electric 
fluids  striving  to  re-unite.  These  effects  are  designated  by  the 
term  of  re- action.  The  experiment  will  be  tried  to  no  purpose 
on  a  frog  that  has  already  been  killed  five  or  six  hours,  but  it  will 
succeed  very  well  with  one  immediately  after  it  has  been  killed, 
or  better  still  with  the  living  animal. 

In  the  vicinity  of  a  powerful  machine,  even  a  man  will  receive 
similar  shocks  when  standing  in  communication  with  the  ground. 
The  discharges  of  thunder- clouds  act  in  like  manner,  that  is,  by  a 
direct  shock,  and  by  re-action. 


402  GALVANISM. 


PAET  III. 

GALVANISM. 

CHAPTER  I. 

ON  ELECTRICITY  OF  CONTACT,  AND  ON  THE  GALVANIC  CIRCUIT. 

IN  the  year  1789,  Galvani  made  a  discovery  at  Bologna,  by 
which  a  new  field  was  opened  to  Physics.  This  discovery  was  the 
observation  of  the  seemingly  unimportant  fact,  that  the  freshly 
prepared  limbs  of  frogs,  suspended  by  copper  hooks  to  an  iron 
rod,  were  convulsed  as  often  as  the  muscles  of  the  thigh  were 
brought  into  contact  with  the  iron-railing  by  the  wind,  or  any  other 
cause.  The  copper  hook  was  in  contact  with  the  crural  nerve. 

It  was  at  first  supposed  that  this  phenomenon  could  be  explained 
by  the  existence  of  a  kind  of  nervous  fluid,  similar  to  the  electric 
fluid;  the  organic  body  was  regarded  as  a  kind  of  Leyden  jar 
with  respect  to  this  fluid,  the  nerves  serving  as  the  coating  on  the 
one  part,  and  the  muscles  on  the  other.  A  discharge  ought  to  take 
place  as  soon  as  the  nerves  and  muscles  were  brought  in  connect- 
ing communication  with  each  other,  as  seen  in  the  experiments  of 
Galvani,  with  the  copper  hooks  and  iron- railings. 

.Alexander  Volta  repeated,  with  unwearied  attention,  the  experi- 
ments of  Galvani,  and  soon  found  that  a  circumstance  had  hitherto 
been  wholly  overlooked  in  the  experiment,  which  was  very  essen- 
tial to  its  success.  For  instance,  to  obtain  a  strong  effect,  it  was 
indispensable  that  the  circuit  of  connection  between  the  nerves  and 
muscles  should  consist  of  two  different  metals  in  contact  with  each 
other.  He  made  the  experiment,  as  represented  in  Fig.  388.  One 
part  z  of  the  connection  is  zinc,  the  other  k  copper.  Both  metals 
must  have  a  perfect  metallic  surface  at  the  place  where  they  come 


GALVANISM.  403 

into  contact  with  each  other,  and  where  they  touch  the  limb  of  the 
frog.  Volta  concluded  from  his  experiments,  that  the  leg  of  the 
frog  was  not  to  be  regarded  as  aLeyden  jar;  that  the  fluid  acting 
here  was  not  developed  either  in  the  3gg 

nerves  or  muscles,  but  by  the  contact 
of  the  two  metals,  and  that  it  was  per- 
fectly identical  with  the  common  elec- 
tric fluid.  These  views  were  contested 
by  Galvani  and  his  adherents,  each 
party  seeking  to  confirm  the  correctness 
of  his  theory  by  new  experiments, 
until,  at  length,  Volta's  opinions  were 
generally  received  and  adopted. 

Direct  Proofs  of  the  Development  of  Electricity  by  Contact. — 
The  idea  that  electricity  could  be  developed  by  the  mere  contact 
of  heterogeneous  bodies,  only  gained  credit  by  degrees,  the  severity 
of  science  requiring  direct  and  convincing  proofs;  these  were, 
however,  soon  afforded  by  Volta,  by  the  aid  of  an  apparatus  in- 
vented by  him  some  years  previously,  viz.,  the  conductor  with 
which  we  have  already  become  acquainted.  The  experiment  he 
made,  is  conducted  in  the  following  manner.  After  having  ascer- 
tained that  the  condenser  screwed  to  the  gold-leaf  electromotor, 
Fig.  389,  will  hold  a  charge  well,  and,  after  restoring  it  to  its 
natural  state,  we  place  with  the  other  Fi  3g9 

finger  the  upper  plate  in  connection 
with  the  ground,  while  the  other 
plate  is  touched  by  a  piece  of  zinc, 
also  in  connection  with  the  ground, 
by  being  held  in  the  other  hand.  It 
follows,  of  course,  that  the  surfaces 
of  the  plates  of  the  condenser  must 
not  be  varnished  where  they  are  not 
in  contact  with  each  other,  other- 
wise there  could  be  no  metallic  con- 
tact between  the  zinc  and  the  brass 
(which  is  almost  the  same  in  this 
case  as  pure  copper)  of  one  of  the  plates  of  the  condenser.  If  we 
now  withdraw  the  finger  from  the  upper,  and  the  zinc  from  the 
lower  plate,  after  the  contact  has  lasted  for  a  minute  or  so,  and 
then  lift  off  the  upper  plate  of  the  condenser,  we  shall  perceive  a 


404 


GALVANISM. 


decided  divergence  of  the  gold  leaves.  Whence  comes  this  elec- 
tricity? It  can  evidently  arise  only  from  the  contact  of  the  zinc 
and  copper  of  the  lower  plate  of  the  condenser ;  here  there  is  an 
especial  force  at  work  to  separate  the  fluids  and  put  them  into 
motion ;  the  positive  electricity  will  pass  to  the  zinc,  and  from 
thence  into  the  ground ;  while  the  negative,  on  the  contrary,  will 
be  driven  to  the  lower  brass,  or  copper  plate,  and,  combined  there, 
while  it  acts  decomposingly  upon  the  upper  plate.  If,  now,  the 
latter  be  raised  up,  the  combined  —  electricity  in  the  lower  plate 
can  diffuse  itself,  and  thus  effect  the  divergence  of  the  gold  leaf. 
If  we  vary  the  experiment  by  touching  the  upper  plate  of  the 
condenser  with  the  zinc,  and  the  lower  with  the  finger,  the  gold 
leaf  will  diverge  with  +  electricity. 

The  development  of  electricity  by  the  contact  of  different 
metals  may  be  still  better  shown  by  help  of  Bohnenberger's  elec- 
troscope. The  accompanying  Fig.  390  represents,  according  to 
Fechner's  views,  the  best  form  for  this  instrument. 

In  a  horizontal  glass  tube  there 
is  inserted  a  so-called  dry  or  Zam- 
boni's  pile,  the  properties  of  which 
we  shall  consider  at  a  subsequent 
period  ;  the  glass  tube  is  closed  at 
its  extremities  by  metal  caps,  from 
which  pass  metal  wires  e  and  /, 
terminating  in  the  plates  x  and  y. 
Zamboni's  pile  has  this  property, 
that  one  end  is  always  positively,  and  the  other  negatively  elec- 
tric ;  consequently  one  plate  x,  for  example,  will  always  be  charged 

with  — ,  and  the  other  with  +  elec- 
tricity. 

A  Zamboni's  pile  of  this  kind  is 
fixed  in  a  wooden  box,  Fig.  391,  in 
the  upper  part  of  which  there  is  an 
aperture  for  the  passage  of  the  poles 
x  and  y. 

If,  now,  we  suppose  a  piece  of  gold 
leaf  suspended  midwaybetween  these 
poles  it  will  remain  at  rest,  being 
equally  strongly  attracted  by  both 
poles;  on  charging  it  slightly  with 


Fig.  391. 


SCALE   OF   TENSION.  405 

positive  electricity,  it  will,  however,  draw  nearer  the  negative 
pole,  and,  vice  versa,  it  will  approach  the  positive  pole  on  being 
charged  negatively. 

A  strip  of  gold  leaf  is  suspended  between  the  two  poles;  and 
being  fastened  to  a  metal  rod  inserted  in  a  glass  tube,  is  insulated 
in  the  same  manner  as  the  rod  to  which  hang  the  pendulums 
represented  in  Fig.  389 ;  here  also  the  gold  is  within  the  glass 
vessel  to  prevent  the  disturbing  action  of  currents  of  air. 

We  may  screw  metal  plates  to  the  upper  end  of  the  metal  stem 
holding  the  gold  leaf.  Let  us  assume  that  a  perfectly  smooth 
copper  plate  of  good  metallic  surface  has  been  screwed  on ;  on 
placing  upon  this  copper  plate  a  similar  zinc  plate,  with  an  equally 
good  metallic  surface,  a  discharge  will  follow  as  soon  as  we  lift 
off  the  zinc  plate,  showing  that  the  copper  plate  was  negatively 
electric. 

If  the  zinc  plate  had  been  screwed  on  the  instrument,  a  dis- 
charge towards  the  negative  pole  would  have  followed  the  removal 
of  the  copper-plate,  because  the  zinc  had  become  positively  elec- 
trified by  contact  with  the  copper. 

This  experiment  shows,  then,  not  only  that  electricity  is  deve- 
loped by  the  contact  of  copper  and  zinc  (copper  becoming  nega- 
tively, and  the  zinc  positively  electric),  but  also,  that  the  largest 
amount  of  developed  electricity  remains  combined  at  the  surfaces 
of  contact  between  the  two  metals,  and  that  a  proportionately 
small  part  is  freely  distributed  over  the  metal  plates,  since  the 
discharge  does  not  follow  till  after  the  raising  of  the  other  plate. 

Such  an  excitement  of  electricity  occurs  almost  universally, 
when  heterogeneous  substances  come  into  contact  with  each  other; 
it  furnishes,  however,  some  of  its  most  striking  illustrations  with 
the  metals.  The  unknown  cause  of  the  development  of  electri- 
city by  the  contact  of  heterogeneous  substances,  is  termed  the 
electromotor  power. 

Scale  of  Tension. — The  electric  tensions  developed  by  the  elec- 
tromotor force,  and  distributed  over  the  bodies  in  contact,  is  not 
equal  for  all  substances.  Metals  are  good  electromotors,  but  even 
among  them  we  observe  a  great  difference  in  this  respect.  For 
instance,  zinc  will  become  much  more  strongly  charged  with  + 
electricity  when  in  contact  with  platinum  than  with  copper;  cop- 
per will  become  negatively  electric  when  brought  into  contact 
with  zinc,  and  positively  so  when  in  connection  with  platinum. 


406  SCALE    OF    TENSION. 

The  following  table  exhibits  a  series  of  bodies  so  arranged,  that 
each  preceding  one  becomes  positively  electric  when  in  contact 
with  all  the  succeeding  ones. 

+ 

Zinc 

Lead 

Tin 

Iron 

Copper 

Silver 

Gold 

Platinum 

Charcoal 

The  electric  difference  between  zinc  and  copper,  and  that  be- 
tween copper  and  platinum,  are,  together,  equal  to  the  electric 
difference  between  zinc  and  platinum,  that  is,  if  we  lay  a  copper 
plate  upon  a  zinc  plate,  and  a  platinum  plate  on  the  former,  the 
electric  tension  of  the  extreme  plates  will  be  precisely  as  great  as 
if  the  platinum  and  zinc  plates  lay  immediately  over  each  other. 
All  bodies  in  the  above  given  series  bear  the  same  relation  to  each 
other ;  for,  if  we  place  three  layers  together,  the  electric  tension  of 
the  extreme  plates  will  always  be  the  same  as  if  they  were  in 
immediate  contact,  and  there  were  no  intervening  plates. 

The  same  holds  good  with  respect  to  4,  5,  or  more  metal  plates 
ranged  the  one  above  the  other ;  the  tension  of  the  extreme  plate 
will  be  the  same  as  if  there  were  no  intervening  plates.  All  metals 
assume  a  decided  position  in  this  scale  of  tension ;  charcoal  being, 
in  this  respect,  entirely  similar  to  a  metal,  and  more  electro- 
negative than  platinum.  Many  compound  bodies  also  assume  a 
definite  place  in  this  scale,  as,  for  instance,  binoxide  of  manganese, 
oxide  of  iron,  sulphuret  of  iron,  sulphuret  of  lead,  &c. ;  but  other 
compound  bodies,  as  fluids,  do  not  obey  the  laws  of  such  a  scale 
of  tension. 

Zinc  will  become  negatively  electric  in  contact  with  pure  water, 
but  now,  if  we  put  water  into  this  scale  of  tension,  we  must,  from 
its  relation  to  this  metal,  place  it  over  zinc.  If  water  really  took 
this  position,  platinum  would  become  much  more  strongly  nega- 
tive than  zinc  in  contact  with  water.  Experience,  however,  shows 
the  contrary  to  be  the  case,  platinum  becoming  actually  much  less 


CONSTRUCTION   OF   THE   VOLTAIC   PILE.  407 

negatively  excited  than  zinc ;  we  see,  therefore,  that  water  is  a 
body  that  does  not  obey  the  laws  of  this  scale  of  tension.  Diluted 
sulphuric  acid  exhibits  a  similar  relation,  exciting  zinc  and  copper 
negatively,  the  former,  however,  much  more  strongly  than  the 
latter  body;  platinum  and  gold  are  positively  excited  by  diluted 
sulphuric  acid. 

The  peculiar  property  of  many  fluids,  which  prevents  us  from 
ranking  them  in  the  scale  of  tension,  enables  us  to  produce  a 
stronger  electric  tension  in  moist  conductors  by  layers  of  metal 
plates,  than  can  be  excited  by  two  metal  plates  in  contact  with  one 
another ;  we  shall  see  this  more  plainly  exemplified  in  the  voltaic 
pile,  which  we  are  about  to  consider. 

Construction  of  the,  Voltaic  Pile. — Three  different  bodies  are 
used  in  the  construction  of  the  voltaic  pile:  viz.,  two  metals,  and 
a  third  body  having  no  place  in  the  scale  of  tension. 

The  metals  generally  used  are  copper  and  zinc,  two  bodies  re- 
motely separated  in  the  scale  of  tension:  zinc  forms  the  positive, 
and  copper  the  negative  element.  A  copper  and  a  zinc  plate  are 
usually  soldered  together. 

The  third  element  of  the  voltaic  pile  is  a  moist  disc,  that  is,  a 
piece  of  cloth,  or  pasteboard,  saturated  with  pure  water,  a  very 
dilute  acid,  or  a  solution  of  salt. 

Let  a  copper  plate,  which  is  a  negative  element,  be  placed  in 
connection  with  the  ground  by  means  of  a  copper  wire/,  Fig.  392, 
an  equally  large  zinc  plate  being  laid  Fig  392 

upon  its  upper  surface.  By  the  electro- 
motor force,  the  zinc  will  become  posi- 
tively, and  the  copper  negatively  electri- 
fied ;  but  the  liberated  electricity  will  pass 
off  into  the  ground,  whilst  there  will  re- 
main upon  the  zinc  plate  liberated  electricity,  the  density  of  which 
will  depend  upon  the  electric  difference  between  copper  and  zinc. 
If  we  assume  this  density  as  a  unity,  we  may  say  that,  under  these 
circumstances,  the  density  of  the  liberated  electricity  upon  the 
copper  is  0,  while  liberated  -f  electricity  of  the  density  1  distri- 
butes itself  over  the  zinc.  If,  now,  by  any  means  a  portion  of  the 
liberated  electricity  were  withdrawn  from  the  zinc,  so  that  its 
density  became  less  than  1,  the  loss  +  electricity  experienced  by 
the  zinc  plate  would  be  immediately  compensated  for  by  the  elec- 
tromotor force,  while  an  amount  of  —  electricity,  fully  equal  to 


408  CONSTRUCTION    OF    THE    VOLTAIC    PILE. 

the  newly  developed  +  electricity  passing  to  the  zinc  plate,  would 
be  communicated  to  the  copper  plate,  and  thence  to  the  ground. 
We  must  now  lay  a  piece  of  moist  cloth  upon  the  zinc.  Let  us 
then  assume,  for  the  sake  of  simplifying  the  matter,  that  this  ex- 
ercises no  electromotor  force  when  in  contact  with  zinc,  acting 
merely  as  a  conductor,  then  a  portion  of  liberated  +  electricity 
will  pass  from  the  zinc  to  the  moist  cloth,  the  loss  being,  however, 
immediately  supplied,  so  that  the  density  of  the  liberated  -f  elec- 
tricity on  the  zinc  will  remain  at  1,  while  the  liberated  -f  electri- 
city of  the  density  1  will  likewise  distribute  itself  over  the  damp 
cloth.  If,  then,  a  copper  plate  be  again  laid  on  the  moist  piece 
of  cloth,  +  electricity  will  then  distribute  itself  over  it,  and  attain 
a  density  1.  We  shall  now  have,  therefore,  on  the  under  copper 
plate  a  density  of  0,  and  +  electricity  of  a  density  =  1  on  the 
zinc  plate,  the  moist  cloth,  and  the  upper  copper  plate. 

If  we  lay  a  zinc  plate  upon  the  upper  copper  plate,  the  former 
will  be  charged  with  free  -f  electricity  of  the  density  1,  even  if 
there  be  no  electromotor  force  at  work ;  the  electric  difference 
between  copper  and  zinc  will,  however,  remain  still  the  same, 
being,  according  to  our  previous  showing,  always  =  1 ;  if,  there- 
fore, the  upper  copper  plate  have  +  electricity  of  the  density  1, 
the  density  of  the  -f  electricity,  on  the  superposed  zinc  plate, 
must  be  =  2. 

In  the  same  manner,  we  may  further  conclude,  that,  on  laying 
upon  the  second  zinc  and  copper  layer  another  moist  cloth,  and 
then,  again,  a  copper  and  zinc  plate,  in  the  same  order,  the  copper 
being  above  the  zinc  plates,  the  density  of  the  liberated  +  elec- 
tricity, on  this  third  layer,  will  be  =  3.  If  we  continue  to  pile 
the  elements  in  the  same  order,  namely,  copper,  zinc,  and  moist 
pieces  of  cloth,  the  freed  +  electricity  upon  the  4th,  5th  . .  .  100th 
zinc  plate,  will  have  a  density  =  4,  5  ...  or  100. 

The  above  described  arrangement  is  called  the  voltaic  pile,  from 
the  name  of  its  inventor,  and  is  represented  in  Fig.  393,  as  con- 
sisting of  20  pairs  of  plates.  The  stand  is  made  of  dried  wood, 
the  pillars  supporting  the  pile  of  glass. 

The  one  end  of  the  pile  is  called  the  zinc  end,  from  the  plate 
terminating  the  series,  or,  also,  the  positive  pole,  and  the  other  is 
the  copper  or  negative  pole.  In  the  previously  described  arrange- 
ment, the  negative  pole  was  in  connection  with  the  ground,  the 
positive  one  insulated,  while  +  electricity  was  distributed  over 


THE    INSULATED    PILE. 


409 


the  whole  pile,  the  density  increasing  from  FJg-  393. 

below  upwards,  according  to  our  considera- 
tions. If  the  negative  pole  be  insulated,  and 
the  positive  one  put  into  connection  with  the 
ground,  the  density  of  the  liberated  electricity, 
upon  the  zinc  end,  will  be  0,  whilst  —  elec- 
tricity will  be  distributed  over  the  whole  pile, 
its  density  increasing  towards  the  copper  end. 
The  Insulated  Pile. — Let  us  assume  that  we 
have  one  pile,  consisting  of  100  double  plates, 
whose  negative  pole  is  in  connection  with  the 
ground,  and  another,  precisely  similar  to  the 
former,  with  the  exception  of  its  positive  pole, 
communicating  with  the  ground.  If,  now,  we 
put  the  two  piles  together  in  such  .a  manner 
that,  by  the  interposition  of  a  piece  of  wetted 
cloth,  the  two  discharging  poles  may  touch 
each  other  (that  is,  the  +  pole  of  the  one  pile, 
and  the  —  pole  of  the  other),  we  shall  have 
a  single  pile  of  200  double  plates,  the  halves 
of  which  will  be  still  in  the  same  condition  as  before ;  even  on 
interrupting  the  conducting  communication  with  the  ground. 
The  middle  will  be  consequently  in  its  natural  condition,  even 
when  the  connection  with  the  earth  has  ceased.  The  one-half 
will  be  positively,  and  the  other  half  negatively  charged,  the 
strength  of  the  charge  increasing  from  the  middle  towards  the 
poles.  The  electric  tension,  at  each  pole,  will  be  precisely  the 
same  as  at  the  insulated  pole  of  a  pile  of  100  double  plates,  where 
the  opposite  pole  has  been  connected  with  the  ground.  If  we 
disturb  this  equilibrium,  by  taking  away  a  portion  of  electricity 
from  one  pole,  the  tension  will  be  diminished  here,  while  it  will 
increase  at  the  opposite  pole ;  and  the  point  of  the  pile,  still  in  a 
natural  condition,  will  be  moved  more  and  more  from  the  middle, 
towards  the  pole  from  which  electricity  has  been  withdrawn.  If, 
however,  the  whole  pile  remains  insulated,  the  former  condition 
will  be  gradually  restored ;  that  is  to  say,  the  condition  of  equili- 
brium will  gradually  return  to  the  middle,  because  there  will  be 
Constantly  a  larger  discharge  of  electricity  passing  from  the  more 
strongly  charged  pole.  Electric  equilibrium  is,  therefore,  restored 

in  each  thoroughly  insulated  pile,  in  such  a  manner  that  the  mid- 
op; 


410  THE    CLOSED    AND    DRY    PILE. 

die  is  in  a  natural  condition,  while  the  two  halves  are  charged 
with  opposite  electricity,  the  density  of  which  increases  from  one 
pair  of  plates  to  the  other  towards  the  poles. 

The  Closed  Pile. — As  the  two  poles  of  an  insulated  pile  are 
always  sources  of  opposite  electricity,  it  is  clear,  that  if  we  join 
to  each  pole  a  wire,  each  of  these  wires  will  become  charged  with 
the  electricity  of  its  pole.  We  thus  procure  a  positively  and  a 
negatively  charged  conductor ;  if  the  two  conductors  be  brought 
into  contact  with  each  other,  a  constant  reunion  of  the  electricities, 
developed  in  the  pile,  must  take  place.  This  is  shown  in  Fig, 
393.  On  bringing  the  two  wires  (often  called  the  two  poles] 
within  a  short  distance  of  each  other,  we  see  an  uninterrupted 
current  of  sparks  pass  from  the  one  to  the  other. 

If  we  bring  the  two  conducting  wires  into  immediate  contacl 
with  each  other,  that  is,  if  we  close  the  circuit,  the  passage  oj 
sparks  will  cease,  although  all  electrical  action  will  not  be  wholl) 
destroyed  on  that  account.  Electricity  is  continuously  developed 
in  the  pile,  and  a  reunion  of  the  electricities,  separated  in  the 
pile,  is  continuously  taking  place  at  all  points  of  the  closing  wire 
While  everything,  therefore,  appears  at  rest  externally,  there  are 
internally  continual  activity  and  motion. 

This  electric  current  is  capable  of  producing  very  powerfu 
effects  upon  the  nerves,  of  making  metal  wires  red  hot,  the  mag- 
netic needle  deviate,  and  of  occasioning  chemical  decomposi- 
tions. We  shall  soon  proceed  to  the  consideration  of  some  o 
these  actions. 

The  Dry  Pile. — In  dry  piles,  the  electromotors  are  likewise  me- 
tallic substances ;  but  the  conducting  medium,  separating  ever] 
two  pairs,  is  not  a  fluid,  but  some  solid  body,  which  is  either  per- 
fectly dry,  or  only  partially  damp.  Among  the  different  appa- 
ratuses of  this  kind  that  have  successively  been  suggested,  that  o 
Zamboni  appears  the  most  efficacious.  On  a  piece  of  commor 
writing  paper,  exactly  as  moist  as  it  would  be  if  left  to  itself  ir 
damp  weather,  we  fix,  with  gum  or  starch,  on  one  side,  silve 
leaf  (zinc),  while  we  rub  finely  pulverized  manganese  (binoxidi 
of  .manganese)  on  the  other,  with  a  cork;  several  sheets  of  paper 
thus  prepared,  are  then  laid  over  one  another,  and  cut  with 
stamp  into  round  pieces  from  10  to  15  lines  in  diameter.  Pile 
of  from  1000  to  2000  double  plates  are  now  made  from  thes 
round  discs,  which  must,  however,  be  carefully  piled  up  in  th 


PROPERTIES    OF    THE   DRY    PILE.  411 

same  order,  so  that  the  zinc  sides  are  all  turned  either  upwards 
or  downwards.  The  pile  must  be  compressed,  in  order  to  secure 
a  perfect  connection  between  the  metal  plates,  after  sufficiently 
strong  metal  plates,  having  3  or  4  projecting  parts,  have  been 
attached  to  the  extremities,  and  joined  together  with  silk  cords. 
The  pile  is  rubbed  over  with  melted  sulphur,  or  shell-lac,  to  pro- 
tect it  from  the  influence  of  the  weather. 

We  may,  also,  form  these  dry  piles  from  gold  and  silver  paper. 
For  this  purpose,  we  glue  together,  on  the  paper  sides,  a  sheet  of 
fictitious  gold  leaf  (copper),  and  a  sheet  of  fictitious  silver  leaf 
(tin),  so  that  we  obtain  a  piece  of  paper,  covered,  on  the  one  side, 
with  copper,  and,  on  the  other,  with  tin.  From  the  paper,  thus 
prepared,  the  discs  are  cut. 

Properties  of  the  Dry  Pile. — A  Zamboni's  pile  of  2000  plates 
is  unable  to  give  the  least  shock,  or  produce  the  least  chemical 
decomposition,  notwithstanding  that  its  poles  show  a  marked 
tension.  Even  a  pile  of  100  or  200  double  plates  produces 
divergence  in  a  gold  leaf  electromotor,  without  the  use  of  a  con- 
denser ;  and,  to  effect  this,  it  is  only  necessary  to  hold  one  pole 
in  one  hand,  while  we  touch,  with  the  other  hand,  the  plate  or 
the  ball  of  the  electromotor.  We  obtain  a  very  considerable 
divergence  with  piles  of  from  800  to  1000  double  plates. 

If  we  touch  one  coating  of  a  Franklin  plate  with  the  pole  of 
such  a  pile,  whilst  the  other  pole  is  connected  with  the  ground, 
we  may  often  succeed  in  imparting  so  strong  a  charge  to  the  plate 
as  to  cause  the  emission  of  a  spark  by  its  discharge. 

If  both  poles  of  the  pile  be  insulated,  the  opposite  electricities 
will  soon  accumulate,  in  equal  proportions,  at  the  poles ;  the  ten- 
sion increasing  here  until  the  quantity  of  electricity  lost,  by  each 
pole,  in  a  given  time,  through  the  action  of  the  atmosphere,  is 
equal  to  the  quantity  again  imparted,  in  the  same  space  of  time,  to 
the  pole  by  the  pile.  From  this  moment,  the  tension,  at  the  poles, 
remains  constant.  If,  now,  the  air  be  more  moist,  the  electric 
loss,  at  the  poles,  will  amount  to  a  larger  fraction  of  the  electricity 
accumulated  there,  whilst  the  amount  of  electricity,  conveyed  to 
the  pole,  will  remain  the  same ;  hence,  it  follows  that  the  tension, 
at  the  poles,  must  be  less  in  damp  air  than  in  a  dry  state  of  the 
atmosphere. 

If  we  arrange  two  Zamboni's  piles  side  by  side,  in  such  a  man- 
ner that  the  positive  pole  of  the  one,  and  the  negative  pole  of  the 


• 

412  DIFFERENT    FORMS    OF    GALVANIC    CIRCUIT. 

other  are  directed  upwards,  a  light  pendulum  will  constantly 
oscillate  between  the  two  poles.  On  this  principle  is  grounded 
the  so-called  perpetual  motion. 

A  piece  of  gold  leaf  suspended  between  two  Zamboni's  piles, 
will  incline  first  towards  one  and  then  towards  the  other  pole, 
provided  it  be  but  feebly  charged  with  either  kind  of  electricity. 
Instead  of  the  two  vertical  piles,  we  may  make  use  of  a  horizontal 
one,  whose  poles  are  connected,  by  means  of  conducting  wires, 
with  two  metal  plates  standing  opposite  to  each  other,  and  thus 
we  shall  obtain  the  apparatus  described  at  pages  403  and  404. 

Different  forms  of  the  Galvanic  Circuit. — All  forms  of  apparatus 
serving  to  produce  a  continual  electric  current,  are  termed  galvanic 
circuits.  They  are  generally  constructed  of  two  metals  and  one 
fluid.  The  voltaic  pile  formerly  described  was  the  first  apparatus 
of  the  kind;  the  form  offers,  however,  many  objections.  The 
lower  layers,  for  instance,  are  more  strongly  compressed  by  the 
weight  of  the  upper  layers  ;  the  damp  discs  are  thus  dried  while 
the  fluid  escapes  at  the  side  of  the  pile;  by  which  means,  a  con- 
ducting communication  is  established  between  the  separate  pairs 
of  plates  highly  injurious  to  the  combined  effect  of  the  whole. 

The  Trough  apparatus,  which  was  in  use  for  a  longer  period,  is 
represented  at  Figs.  394  and  395.  The  separate  elements  consist 

Fig.  394.  Fig.  395.  of  rectangular  plates  of 

copper  and  zinc  soldered 
together.  They  are  laid 
in  parallel  rows  in  a 
wooden  case  b  bf,  whose 
inner  walls  are  covered 
with  a  non-conducting 
coat  of  resin ;  the  pairs  of 

plates  being  so  inserted  that  the  intervals  between  every  two  form 
cells  or  troughs,  which  are  filled  with  acidulated  water.  This 
layer  of  water,  about  3  lines  in  thickness,  supplies  the  place  of 
the  moist  pieces  of  cloth. 

In  other  galvanic  apparatus,  the  fluid  is  put  into  separate  vessels 
or  glasses  ranged  circularly  or  in  a  straight  line.  Each  glass 
contains  one  zinc  and  one  copper  plate  not  in  contact  with  each 
other,  while  every  zinc  plate  is  connected  with  the  copper  plate 
of  the  preceding  glass  by  a  copper  wire  or  copper  band.  To  this 
class  belongs  especially  Wollastori's  battery.  To  understand  the 


THE   TROUGH   APPARATUS. 


413 


construction  of  this  apparatus,  we  must  first  consider  two  double 
plates,  of  which  a  side  view  is  represented  in  Fig.  396,  and  a 
front  one  in  Fig.  397.  The  copper  band  c  s  is  soldered  to  the 


Fig.  396. 


Fig.  397. 


zinc  plate  s  z  at  s\  d  s'  is  the  second  band  of  copper  soldered  at 
s*  to  a  second  zinc  plate.  The  copper  band  cf  sf  is  connected 
with  a  copper  plate,  which  is  entirely  curved  round  the  first  zinc 
plate  without  touching  it. 

A  similar  copper  plate  passes  round  the  second  zinc  plate,  being 
connected  with  the  wire  of  the  negative  pole.     Each  pair  of  plates 
is  immersed  in  a  vessel  filled  with  acidulated  water.     The  first 
zinc  plate  becomes  4-  electric  when  brought  into  contact  with  the 
band  of  copper  c  s;  this  -f  charge  passes  through  the  fluid  to  the 
copper  plate  which  surrounds  the  zinc  plate,  without  touching  it, 
and  from  this  copper  plate,  through  the  band  of  copper,  to  the 
second  zinc  plate,  &c.     This  arrangement  has  great  advantages : 
— 1.  A  copper  surface  is  opposed  to  the  two  surfaces  of  each  zinc 
plate ;  2.  The  stratum  of  intervenous  liquid  through  which  the 
electricity  passes  from  a  zinc  plate  to  the  next  copper  plate,  is 
extremely  thin;  and  3.  From  the  considerable  quantity  of  liquid 
n  each  vessel,  its  nature  is  not  so  rapidly  altered,  as  is  the  case 
with  the  dry  apparatus,  whose  activity  soon  diminishes.     Fig. 
398  gives  a  side,  Fig.  399  a  front  view  of  a  complete  Wollastori's 
)attery,  and  Fig.  400  the  ground-work.     The  whole  number  of 
>airs  of  plates  is  fixed  to  a  wooden  frame,  so  that  they  may  all  be 
lipped  simultaneously  into,  or  taken  out  of  the  liquid.     Water  is 

35* 


414 


THE    TROUGH    APPARATUS. 


the  liquid  generally  used,  to  which  TVth  sulphuric  acid,  and  ^th 
nitric  acid,  is  added.  The  number  of  pairs  of  plates,  and  their 
surface  required,  depend  upon  the  purposes  to  which  the  voltaic 
apparatus  is  applied.  Many  phenomena  may  be  produced  with 
a  battery  of  many  pairs  of  small  size ;  others,  again,  require  a 
single  pair  only,  but  of  considerable  dimensions,  and  with  perfect 
metallic  contact. 


Fig.  398. 


Fig.  399. 


I   I   1   1   I    II    I   i   i 

101! 


Fig.  400. 


Fig.  401. 


Fig.  402. 


The  simple  circuit  shown  in  Figs.  401  and  402,  is  used  for  such 
experiments  as  require  a  large  quantity  of  electricity  in  motion, 

but  of  a  small  degree  of  tension.  C 
is  a  vessel  formed  of  two  cylinders 
of  copper  sheeting  of  different  dia- 
meters, the  one  placed  within  the 
other,  and  so  arranged  that  the  space 
intervening  between  the  two  may  be 
filled  by  the  zinc  cylinder  z9  and  the 
acidulated  water.  A  copper  wire 
ending  in  a  cup  containing  mercury, 
is  soldered  to  the  zinc  cylinder.  A  similar  mercury  cup  is  at- 
tached to  the  copper  vessel.  In  placing  the  zinc  cylinder  within  the 
copper  vessel,  care  must  be  taken  that  the  zinc  does  not  come  in 
contact  with  the  copper.  This  is  most  easily  prevented  by  means 
of  pieces  of  cork.  If  we  wish  to  complete  the  circuit,  we  must 
connect  the  mercury  cups  by  a  metallic  wire.  This  apparatus 
has  this  advantage,  that  it  enables  the  zinc  to  be  very  conveniently 
cleaned. 


HARE'S   CALORIMOTOR. 


415 


Hare's  Calorimotor,  represented  in  Figs.  403  and  404,  is  used 
where  we  have  to  act  upon  a 

large  surface  of  metal  plates.  Fis- 403-  Fig-  404. 

On  a  wooden  cylinder  6,  about 
3  inches  in  diameter,  and 
from  a  foot  to  a  foot  and  a  half 
in  height,  there  are  two  plates, 
one  of  zinc  and  the  other  of 
copper,  rolled  up  in  the  same 
manner,  and  separated  by 
cloth  strips  /.  We  thus  ob- 
tain a  pair  of  plates  of  50  to 
60  square  feet  in  area.  The 
name  Calorimotor  is  applied 
to  this  apparatus  from  its  special  property  of  making  metal  wires 
red  hot,  and  even  fusing  them. 

[The  apparatus,  as  devised  by  Dr.  Hare,  differs  in  form  from 
the  above,  as  may  be  seen  in  Fig.  405.     A  a  are  cubical  boxes, 

Fig.  405. 


one  containing  acidulated,  and  the  other  pure  water ;  b  b  is  a 
wooden  frame  containing  zinc  and  copper  plates,  alternating  with 
each  other,  and  from  i  to  J  an  inch  apart ;  T  T  t  t  are  masses 
of  tin  cast  over  the  protruding  edges  of  the  sheets  which  are  to 
communicate  with  each  other.  The  small  figure  represents  a 
horizontal  section  of  the  series  of  plates,  showing  the  mode  in  which 


416  BECQUEREL'S    CONSTANT    BATTERY. 

the  junction  between  the  sheets  and  the  tin  masses  is  effected. 
Between  z  z,  only  the  zinc  is  in  contact  with  the  tin,  whilst  be- 
tween c  c,  the  copper  alone  is  connected  with  it.  At  the  back  of 
the  frame,  ten  sheets  of  copper  between  c  c,  and  ten  sheets  of  zinc 
between  z  z,  also  communicate  by  a  common  mass  of  tin,  ex- 
tending the  whole  length  of  the  frame  between  T  T\  but,  in 
front,  as  shown  in  the  larger  figure,  there  is  an  interstice  between 
the  mass  of  tin  connecting  the  ten  copper  sheets,  and  that  con- 
necting the  ten  zinc  sheets :  ff  screw  forceps  on  each  side  of  the 
interstice  to  hold  the  wire,  which  is  to  undergo  ignition.  The 
plates  are  separated  by  a  wooden  partition  p  p.  The  swivel  8 
permits  the  frame  to  be  swung  round  after  removal  from  the  acid 
in  Jly  and  to  be  lowered  into  the  pure  water  in  a,  for  the  purpose 
of  washing  off  the  adhering  acid.] 

In  all  the  circuits  we  have  hitherto  described,  whether  simple 
or  compound,  the  action  is  very  energetic  immediately  after  im- 
mersion into  the  acid  fluid,  but  it  very  rapidly  diminishes.  This 
variation  in  the  current  always  occasions  great  disturbance  in 
experiments  made  to  compare  the  force  of  different  currents. 
The  constant  batteries  which  have  lately  come  into  use,  are,  how- 
ever, free  from  this  inconvenience.  We  must  here  limit  ourselves 
to  a  description  of  the  most  important  constant  circuits,  reserving 
for  a  subsequent  occasion  an  exposition  of  the  theory  as  well  as 
the  causes  that  contribute  to  the  rapid  diminution  of  the  force  of 
the  current  in  ordinary  circuits. 

As  inventor  of  the  constant  circuit,  BecquereVs  name  deserves 
mention.  Fig.  406  represents  an  element  of  BecquereVs  constant 

circuit ;  it  consists  of  a  hollow  cylin- 

Fig.  406.  ,         -  ,,.  ,       .. 

der  a  made  of  thin  copper  sheeting, 
loaded  with  some  sand  6,  and  closed 
on  all  sides.  The  bottom  c  is  even, 
the  top  d  conical,  having  over  it  a 
rim  e  perforated  with  numerous  holes. 
The  whole  cylinder  is  surrounded  by 
a  bladder  g,  fastened  to  the  rim  e 
above  the  holes  f.  We  now  pour  a 
solution  of  sulphate  of  copper  on  the 
cone  d,  and  this  running  through  the 
holes  f,  fills  the  space  between  the 
bladder  and  the  cylinder  a;  a  few 
crystals  of  sulphate  of  copper,  (blue  vitriol,)  are  laid  upon  the 


BECQUEREL'S    CONSTANT    BATTERY.  417 

cone  d,  being  gradually  dissolved  by  the  fluid  flowing  over  them. 
The  bladder  is  enclosed  in  a  hollow  cylinder  of  zinc  A,  slit  length- 
wise, so  that  it  may  be  widened  or  contracted  at  will.  This  zinc 
cylinder,  as  well  as  the  bladder  containing  the  copper  cylinder, 
and  the  blue  vitriol  solution,  are  immersed  in  a  vessel  i,  made 
either  of  glass  or  porcelain,  which  contains  dilute  sulphuric  acid, 
or  a  solution  of  sulphate  of  zinc,  or  of  muriate  of  soda.  Two 
strong  copper  wires  p  and  n,  one  of  which  is  soldered  to  the  zinc 
cylinder,  and  the  other  to  the  copper,  form  the  two  poles  of  the 
element.  If  we  establish  a  metallic  connection  between  these 
two  poles,  the  electric  current  will  begin  to  circulate. 

Daniel's  constant  battery  is  only  a  modification  of  BecquereVs 
invention. 

[It  consists,  Fig.  407,  of  a  copper  cell  or  vessel,  forming  the 
negative  metal.  A  rod  of  amalgamated  zinc  is  placed 
within  a  tube  of  porous  earthenware.  Attached  to  each 
metal  is  a  binding  screw,  to  form  connections.  To  put 
this  cell  in  action,  place  the  parts,  as  shown  in  the  figure, 
fill  the  porous  tube  with  a  mixture  of  one  part  of  sul- 
phuric acid,  and  ten  parts  of  water ;  and  the  copper 
cell  with  a  saturated  solution  of  sulphate  of  copper. 
The  perforated  metal  shelf  is  to  support  additional  sul- 
phate to  keep  up  the  strength  of  the  solution.] 

In  the  Bunsen  battery,  the  place  of  the  copper  is  supplied  by 
carbon,  which  is  still  more  negatively  electric,  and  is  used  here 
in  the  form  of  hollow  cylinders.  A  hollow  cylinder  of  this  kind, 
open  at  the  bottom,  5  inches  in  height,  and  2J  inches  in  diameter, 
having  its  sides  about  3  lines  in  thickness,  is  placed  in  a  glass 
vessel,  as  seen  in  Fig.  408,  somewhat  con- 
tracted towards  the  top,  so  as  to  have  no 
great  interstice  between  the  carbon  and 
the  glass,  the  cylinder  standing  conse- 
quently quite  fast  in  the  glass.  We  now 
place  in  the  hollow  of  the  carbon  cylinder, 
a  hollow  cylinder  of  porous  clay,  closed  at 
the  bottom,  and  having,  at  the  height  of 
about  4  inches,  such  a  diameter  as  to  make 
it  fit  into  the  cavity  of  the  carbon  cylinder, 
and  to  leave  a  very  small  space  between  the  clay  and  the  carbon. 
The  clay  cavity  is  filled  with  dilute  sulphuric  acid,  but  the  glass 


418  BECQUEREL'S    CONSTANT    BATTERY. 

contains  so  much  concentrated  nitric  acid,  that  when  the  clay 
cylinder  is  put  in,  almost  the  whole  free  space  of  the  glass  is 
filled  to  the  narrow  neck  of  the  vessel  with  the  last  named  fluid. 
The  upper  end  of  the  carbon  cylinder  projects  beyond  the 
glass,  and  is  slightly  conical,  so  that  a  likewise  slightly  conical 
ring  of  zinc  a  can  be  fastened  to  it.  This  ring  supports,  by  means 
of  a  zinc  brace  6,  a  hollow  zinc  cylinder  c  about  3J  inches  in 
height,  and  1J  inch  in  diameter.  This  cylinder  c  is  suspended 
in  the  clay  cavity  of  the  next  glass  in  the  dilute  sulphuric  acid. 

Fig.  409  clearly  exhibits  the  manner  in  which  one  pair  of  zinc 
plates  is  connected  with  the  next,  the  diagrams  showing  the  out- 
lines   of  four    pairs.      The 
Flg*  409>  carbon  cylinders  are  distin- 

guished by  different  horizontal 
bands.  Within  each  carbon 
cylinder,  we  see  two  white 
rings  in  the  figure  ;  the  outer 
one  represents  the  clay  cy- 
linder seen  from  above,  the 
inner  one,  the  zinc  cylinder. 
The  zinc  cylinder  of  the  first 
glass  is  connected  by  a  strip 
with  the  zinc  ring  encircling 

the  charcoal  cylinder  of  the  second  glass.  In  like  manner,  a  zinc 
strip  connects  the  zinc  cylinder  of  the  second  glass  with  the  zinc 
ring  of  the  third,  and  a  third  strip  joins  the  third  zinc  cylinder 
to  the  fourth  zinc  ring.  The  ring  placed  upon  the  first  carbon 
cylinder  ends  in  a  zinc  strip,  serving  as  a  positive  pole ;  the  zinc 
strip  7i,  with  which  the  zinc  cylinder  terminates  in  the  fourth  glass, 
is  the  negative  pole  of  the  circuit. 

In  the  same  manner,  we  may  construct  circuits  of  any  number 
of  pairs. 

In  each  separate  pair,  the  -f  current  passes  from  the  zinc  ring 
enclosing  the  carbon,  through  the  strip,  to  the  zinc  cylinder  of  the 
next  glass,  from  the  latter,  through  the  dilute  sulphuric  acid,  the 
pores  of  the  clay  cavity,  and  the  nitric  acid  to  the  next  piece  of 
carbon,  &c. 

The  carbon  used  for  the  cylinders,  is  prepared  in  a  peculiar 
manner  from  coal  and  coke  ;  but  we  cannot  enter  here  into  an 
exposition  of  the  process. 


PHYSIOLOGICAL   ACTION   OF   GALVANIC   PILES.  419 

Grove's  battery  is  very  similar  in  its  construction  to  Bunsen's, 
the  difference  between  them  being  principally  that,  in  the  former, 
platinum  is  used  instead  of  carbon. 


CHAPTER   II. 

ACTIONS  OF  THE  GALVANIC  CURRENT. 

Physiological  Actions  of  Galvanic  Piles. — The  convulsions  of 
the  nerves  produced  by  the  electricity  of  the  voltaic  piles,  are  not 
less  violent  than  those  occasioned  by  common  electric  batteries  ; 
their  intensity  depending  upon  the  number  of  pairs  of  plates,  that 
is,  upon  the  amount  of  tension.  To  conduct  the  charge  of  the 
piles  through  the  human  body,  it  is  necessary  to  moisten  the  hands, 
as,  for  instance,  with  salt  water,  the  epidermis  being  a  very  bad 
conductor.  On  touching  both  poles  of  a  pile  of  20  to  30  pairs  of 
plates  with  dry  fingers,  we  do  not  experience  the  slightest  shock, 
but  the  charge  is  perceptible  the  instant  we  wet  the  hands.  The 
charge  of  a  pile  of  80  to  100  pairs  of  plates  is  very  marked. 

We  feel  a  shock  at  the  moment  in  which  we  close  the  circuit 
with  the  fingers;  as  long  as  it  remains  closed,  the  electric  current 
circulates  through  the  body  without  producing  any  very  marked 
action  upon  the  feelings,  and  it  is  only  with  very  powerful  piles 
of  many  pairs  of  plates  that  one  is  conscious  of  a  burning  tingling 
sensation  at  the  places  where  the  current  enters  the  body.  A 
second  shock  is  felt,  however,  at  the  moment  in  which  the  current 
is  re-opened ;  but  this,  termed  the  separation  shock,is  much  weaker 
than  the  closing  shock. 

Even  a  simple  current  will  make  a  lightning-like  appearance 
flash  before  the  eyes.  We  may  make  the  experiment  in  various 
ways  ;  thus,  for  instance,  we  may  bring  a  silver  plate  towards  the 
pupil  of  the  eye,  or  towards  the  eye-lid,  which  must  be  previously 
well  moistened,  and  then  touch  the  plate  with  a  piece  of  zinc  held 
in  the  moistened  hand,  or  retained  in  the  mouth.  On  conducting 
the  current  of  a  pile  through  the  eyes,  the  appearance  of  light 
will  be  stronger. 

If,  also,  we  lay  a  piece  of  zinc  above,  and  a  piece  of  silver  under 


420  GENERATION    OF    LIGHT    AND    HEAT. 

the  tongue,  and  then  bring  the  upper  extremities  of  both  metals 
in  contact,  we  shall  perceive  a  peculiarly  bitter  taste. 

Generation  of  Light  and  Heat  by  Galvanic  Currents. — Galvanic 
currents,  like  the  electricity  of  friction,  produce  heat  and  light. 

If  we  conduct  a  galvanic  current  through  a  metal  wire,  this  will 
be  heated  ;  the  connecting  wire  must,  however,  be  very  short  and 
thin,  to  yield  a  powerful  action.  The  intensity  of  the  heat  will 
depend  upon  the  size,  and  not  on  the  number  of  the  metal  plates. 
To  make  metallic  wires  red  hot,  it  is  only  necessary  to  use  a  sim- 
ple current  of  large  surface,  as  represented  in  Fig.  410.  A  Bun- 
sen's  battery  is  also  well  adapted  for  this  experiment.  The  larger 
Fig.  410.  the  acting  surface  of  the  galvanic  apparatus,  the 

greater  may  be  the  thickness  of  the  wires  that  are 

to  be  made  red  hot  and  melted. 

Iron  and  steel  wire  attain  a  white  heat,  melt,  and 

burn  with  the  emission  of  vivid  sparks. 

Platinum  wires  become  vividly  glowing,  and  melt 

away,  if  they  are  made  short  and  thin  enough  for 
the  circuit  used  in  the  experiment. 

Thin  gold-leaf  volatilizes,  and,  as  one  cannot  use  it  for  touching 
the  poles,  without  its  being  converted  into  vapor  at  the  place  of 
contact,  the  current  is  constantly  interrupted  and  again  closed,  by 
which  means  we  see  emitted  a  number  of  small,  shining  sparks 
of  a  greenish  color.  Silver  tissue  exhibits  the  same  phenomena. 
If  we  fasten  to  each  of  the  poles  of  a  galvanic  circuit,  pointed 
pieces  of  carbon  (of  the  kind  and  size  used  in  the  carbon  cylin- 
ders of  Rumen's  battery),  we  shall,  as  soon  as  these  points  come 
into  contact,  perceive  an  uncommonly  glittering  light.  This  bright 
light  can  be  seen  by  a  Burners  battery  of  only  four  elements ;  a 
small,  brightly  luminous  star  appearing  where  the  points  of  the 
charcoal  come  into  contact  with  each  other.  By  increasing  the 
number  of  the  elements,  the  splendor  of  the  appearance  consider- 
ably increases ;  and  thus,  in  a  circuit  consisting  of  from  30  to  50 
elements,  we  may  obtain  a  light  far  exceeding  in  brightness  Drum- 
mond's  hydro-oxygen  light.  By  the  application  of  this  number  of 
pairs -of  plates,  we  may  remove  the  points  of  the  pieces  of  carbon 
tolerably  far  from  each  other,  if  only  the  current  passes,  and  we 
may  thus  obtain  a  splendid  bow  of  light,  formed  by  the  glowing 
particles  of  the  charcoal  which  pass  from  one  pole  to  the  other. 


CHEMICAL   ACTIONS   OF   THE   VOLTAIC   PILE.  421 

Chemical  Actions  of  the  Voltaic  Pile. — The  first,  and  most  im- 
portant chemical  action  of  the  pile,  was  discovered  by  Carlisle 
and  Nicholson,  at  the  beginning  of  the  present  century,  (30th  of 
April,  1800.)  These  two  natural  philosophers  had  hastily  built 
up  a  pile  of  coins,  zinc  plates,  and  damp  pieces  of  pasteboard, 
in  order  to  repeat  some  of  the  experiments  of  Volta.  After  a  few 
trials,  the  smell  of  hydrogen  became  obvious,  and  Nicholson  was 
led  by  this  to  the  happy  idea  of  suffering  the  current  to  pass 
through  a  tube  filled  with  water,  into  which  fluid  he  plunged  both 
poles,  holding  them  at  some  distance  apart.  The  hydrogen  gas 
soon  rose  to  the  negative  pole  in  small  globules,  whilst  the  zinc 
wire,  connected  with  the  positive  pole,  became  oxidized.  If,  how- 
ever, a  platinum,  or  silver  wire  was  used  in  the  place  of  the  zinc, 
it  did  not  oxidize  ;  but  the  oxygen  likewise  rose  in  bubbles  to  the 
surface.  This  water  was  at  length  directly  decomposed  into  its 
elements.  Cavendish  certainly  had  already  shown  that  oxygen  and 
hydrogen  combine  to  form  water ;  but,  notwithstanding  all  efforts 
made  for  the  purpose,  no  one  had  yet  succeeded  in  accomplishing 
the  direct  decomposition  of  water.  A  suitable  apparatus  for  the 
decomposition  of  water  is  represented  in  Fig.  411.  It  consists  of 
a  glass,  in  the  bottom  of  which  two  platinum  wires 
f  andjf'  are  inserted,  without  being  suffered  to  touch 
each  other.  Two  glass  bells,  o  and  A,  are  filled 
with  water,  and  set  inverted  in  the  glass,  so  that  one 
may  cover  each  of  the  wires.  As  soon  as  the  wires 
f  and  f  are  brought  into  contact  with  the  poles  of 
the  circuit,  bubbles  of  gas  are  developed  in  large 
quantities.  Pure  oxygen  gas  always  rises  in  the 
bell  at  the  -f  pole,  and  hydrogen  gas  at  the  other. 
It  will,  of  course,  be  understood  that  the  water  in  the  bell  must 
not  be  separated  from  that  in  the  vessel,  so  that  the  current  may 
pass  through  the  fluid  from  one  wire  to  the  other. 

The  development  of  gas  will  increase  in  quantity  as  the  dis- 
tance between  the  polar  wires  /and  f  is  diminished,  and  accord- 
ing to  the  amount  of  surface  of  the  metal  standing  in  contact 
with  the  water.  In  many  apparatus,  therefore,  serving  for  the 
decomposition  of  water,  the  wires  have  been  replaced  by  platinum 
plates. 

Distilled  and  perfectly  pure  water  is,  however,  but  slowly  de- 
composed in  this  manner;  but  as  soon  as  we  pour  a  few  drops  of 
36 


422 


CHEMICAL    ACTIONS    OF    THE   VOLTAIC    PILE. 


Fig.  412. 


any  acid,  or  dissolve  a  few  grains  of  salt  in  the  water,  by  which 
the  conducting  power  of  the  fluid  is  considerably  heightened,  a 
very  strong  action  begins,  affording,  in  a  short  time,  a  large 
quantity  of  gas.  We  will  subsequently  consider  how  the  quan- 
tity of  the  gas  developed,  depends  upon  the  force  of  the  current. 
The  apparatus,  shown  in  Fig.  412,  may  be  used  where  we  do 
not  care  to  have  the  two  kinds  of  gas 
separated,  as  it  enables  us  to  decom- 
pose a  larger  quantity  of  water,  owing 
to  the  greater  vicinity  of  two  large 
polar  plates  of  platinum.  The  explo- 
sive gas  escapes  through  a  curved 
tube,  and,  on  immersing  the  opening 
of  the  latter  under  water,  we  may  col- 
lect the  gas,  or  make  the  escaping 
bubbles  detonate. 

The  quantity  of  oxygen  liberated  at 
the  -f  pole,  and  collected  in  the  tube 
o,  (Fig.  411),  has  only  half  the  volume 
of  the  hydrogen  which  is  liberated  at 
the  other  pole,  and  rises  in  the  tube  h. 
The  gases  are,  therefore,  evolved  exactly  in  the  same  proportion 
as  they  combine  with  water.  Water,  as  is  well  known,  consists 
of  1  equivalent  of  oxygen,  +  1  equivalent  of  hydrogen.  But  one 
equivalent  of  hydrogen  occupies,  other  things  being  the  same, 
twice  as  large  a  space  as  one  equivalent  of  oxygen.  The  gases 
evolved  from  the  pile  will,  therefore,  when  combined  together, 
again  yield  water. 

Grotthuss  has  given  the  following  explanation  of  this  remark- 
able phenomenon,  which  is  now  generally  admitted  by  natural 
philosophers  to  be  correct.  When  hydrogen  gas  is  combined 
with  oxygen,  to  form  water,  the  atoms  of  the  oxygen  become  ne- 
gatively electric,  in  the  intimate  connection  established  between 
the  smaller  particles,  while  the  atoms  of  the  hydrogen  are  posi- 
tively electric;  but,  owing  to  the  uniform  distribution  of  the  par- 
ticles of  both  substances,  the  combination  does  not,  of  course, 
exhibit  any  liberated  electricity.  If,  now,  water  be  placed  be- 
tween the  poles  of  a  galvanic  circuit,  the  -f  pole  will  act  in  such 
a  manner,  upon  the  most  contiguous  particles  of  water,  that  the 
—  constituent  will  be  attracted,  and  turned  to  the  -f  pole,  whilst 


*'lg.  413. 


CHEMICAL    ACTIONS    OF    THE    VOLTAIC    PILE.  423 

the  repelled  atom  of  water,  of  the  first  molecule  of  water,  will  be 
turned  away  from  the  -f  pole.  The  water-particle  1,  Fig.  413, 
will  act  upon  the  particle  2,  in  such  a  manner 
as  to  turn  its  elements  to  the  same  side  ;  in  a  m  Flg'  413' 
similar  way,  2  will  act  upon  3,  &c.  It  therefore 
follows,  that  all  the  molecules  of  water  between 
the  two  poles,  will  turn  their  atoms  of  oxygen 
to  the  -f  pole,  and  their  atoms  of  hydrogen  to  the  —  pole,  some- 
what as  shown  in  Fig.  413,  where  the  circle  represents  particles 
of  water,  the  black  half  the  atom  of  hydrogen,  and  the  white 
half  the  atom  of  oxygen.  If,  now,  the  attraction  exercised  by  the 
4-  pole  upon  the  atom  of  oxygen  of  the  water-particle  1,  be 
strong  enough,  it  will  tear  it  violently  from  the  atom  of  hydrogen ; 
this  latter  will  again  combine  with  the  oxygen  of  the  water-parti- 
cle 2 ;  the  hydrogen  of  2,  again  with  the  oxygen  of  3,  &c.  In 
this  manner,  a  constant  decomposition  and  recombination  of  the 
water  will  go  on  along  the  whole  line  between  the  poles,  but  it  is 
only  at  the  poles  that  its  constituents  can  be  liberated. 

A  decomposition  of  water  occurs  in  the  cells  of  the  galvanic 
circuit,  exactly  in  the  same  manner  as  between  the  poles. 

Oxides  are  decomposed  by  the  galvanic  circle  in  the  same 
manner  as  water.  Oxygen  appears  at  the  +  pole,  the  radical  at 
the  —  pole.  The  following  experiment  will  answer  for  metallic 
oxides  that  are  reducible :  if  we  strew  a  little  dry  pulverized  oxide 
upon  a  platinum  plate,  brought  in  connection  with  the  -H  pole  of 
the  pile,  and  touch  the  powder  with  the  —  wire,  we  shall  soon 
see  small  metallic  globules  appear  at  the  extremities  of  the  wire. 
Oxides  less  easy  of  being  reduced  must  be  somewhat  moistened, 
especially  if  they  are  in  a  pulverized  state.  The  water  will 
certainly  also  be  partially  decomposed,  but  this  will  only  serve  to 
increase  the  capacity  for  conducting  electricity.  After  a  time  we 
shall  see,  when  the  pile  is  strong  enough,  small  metallic  globules, 
appearing  at  the  —  pole. 

A  new  epoch  in  science  began  with  the  year  1807,  when  Davy, 
by  means  of  a  galvanic  pile,  made  the  discovery  that  alkalies  could 
be  decomposed,  which  had,  until  then,  been  regarded  as  simple 
bodies.  Alkalies  and  earths  were  thus  ranged  in  the  class  of 
oxides,  and  chemistry  enriched  by  the  acquisition  of  two  new 
metallic  bodies,  potassium  and  sodium.  A  very  strong  battery  is 
necessary  to  decompose  potash.  If  we  make  the  experiment  in 


424  CHEMICAL    ACTIONS    OF    THE    VOLTAIC    PILE. 

the  manner  above  indicated,  we  shall  see  numerous  globules  of 
metal  appear  at  the  negative  pole,  and  again  vanish,  with  the 
emission  of  sparks.  This  is  potassium,  liberated  in  the  decom- 
position of  potash.  Its  affinity  to  oxygen  is,  however,  so  great, 
that  on  being  brought  into  contact  with  the  air,  it  immediately 
oxidizes ;  on  being  brought  into  contact  with  water,  it  abstracts 
the  oxygen,  and  inflames  the  hydrogen  gas,  and  has  the  appear- 
ance of  fire.  Potassium  must,  therefore,  not  be  kept  in  a  fluid 
containing  oxygen.  Petroleum,  or  naphtha,  composed  of  carbon 
and  hydrogen,  is  generally  used  for  this  purpose. 

Seebeck  has  proposed  a  means  by  which  the  potassium  evolved 
by  means  of  a  galvanic  pile,  may  be  collected  with  more  certainty. 
A  hollow  is  made  in  the  piece  of  caustic  potash  we  wish  to  decom- 
pose, and  mercury  poured  into  it.  The  potash  is  then  laid  upon 
a  piece  of  platinum  in  connection  with  the  +  pole  of  the  pile, 
while  the  —  wire  plunges  into  the  mercury.  The  decomposition 
immediately  begins,  the  oxygen  is  liberated  in  the  platinum,  while 
the  potassium,  combining  with  the  mercury,  forms  a  tolerably 
consistent  amalgam.  We  may  then  separate  the  mercury,  by 
distillation  in  an  atmosphere  of  petroleum  vapor,  and  thus  obtain 
the  potassium  in  a  pure  condition. 

Salts  can  also  be  decomposed  by  means  of  the  galvanic  current, 
the  acid  appearing  at  the  +  ,  and  the  earth,  or  base,  at  the  —  pole. 
The  decomposition  of  salts  may  be  made  perceptible  in  the  follow- 
ing manner.     We  fill  a  V-formed  curved  tube  (Fig.  414)  with  a 
saline  solution,  which  is  colored  violet  by  tincture 
of  litmus.     If  now  we  plunge  the  4-  polar  wire 
into  the  fluid  on  the  one  side,  and  the  —  wire  on 
the  other  side,  the  fluid  will  be  red  at  the  +,  and 
blue  at  the  —  pole.     On  changing  the  poles,  the 
original  violet  hue  will  be  only  restored  by  degrees, 
red  appearing  where  the  wire  was  blue  before  the 
inversion  of  the  poles,  and  vice-versa. 

If  we  pour  a  saline  solution  into  two  contiguous 
vessels,  connected  by  a  moist  asbestus  cloth,  or  by 
an  A-shaped  syphon,  filled  with  the  fluid,  and  then  plunge  the  -f 
polar  wire  into  the  one  vessel,  and  the  —  wire  into  the  other,  the 
decomposition  will  go  on  in  the  same  manner ;  and  after  a  time, 
the  acid  will  be  in  the  vessel  into  which  the  -f  wire  has  been  im- 
mersed, and  the  base  in  the  other.  Even  if  we  pour  the  earthy 


CHEMICAL   ACTIONS   OF   THE   VOLTAIC   PILE.  425 

solution  into  the  vessel  JL  containing  the  +  polar  wire,  and  the 
acid  into  the  other  B,  the  acid  will,  after  a  time,  be  in  A,  and 
the  base  in  B.  This  experiment  has  been  modified  in  various 
ways. 

A  saline  solution  is  not  always  decomposed  into  the  acid  and 
base  by  the  galvanic  current,  there  appearing  in  the  decomposi- 
tion, frequently,  only  one  or  other  of  these  bodies.  A  solution  of 
sulphate  of  copper,  for  instance,  is  so  decomposed  that  the  copper 
separates  at  the  —  pole,  whilst  the  oxygen  of  the  oxide  of  copper 
no  longer  remains  in  its  former  combination  on  the  other  side. 
This  decomposition  of  sulphate  of  copper  is  beautifully  exhibited 
in  the  constant  circuit  of  Becquerel  and  Daniel,  already  described. 
When  the  circuit  is  closed,  the  -f  current  passes  from  the  zinc 
through  the  dilute  sulphuric  acid,  then  through  the  solution  of 
sulphate  of  copper  to  the  copper.  If  the  zinc  become  +  electric 
in  contact  with  the  copper,  and  the  latter — ,  the  zinc  is,  of  course, 
the  +,  and  the  copper  the  —  pole,  the  +  current  passes,  there- 
fore, through  the  zinc,  and  the  —  current  through  the  copper  into 
the  fluid.  On  the  one  side  of  the  partition  water  is  decomposed, 
the  oxygen  passes  over  to  the  zinc,  forming  oxide  of  zinc,  which, 
dissolving  in  the  acid,  forms  sulphate  of  zinc.  The  hydrogen  gas 
goes  to  the  partition,  where  it  forms,  as  it  were,  the  +  pole  for 
the  current  passing  into  the  other  fluid.  The  oxide  of  copper  is 
decomposed  by  this  current,  the  oxygen  of  the  oxide  passes  to 
the  +  pole,  consequently,  to  the  wall  of  partition,  where  it  com- 
bines with  the  liberated  hydrogen  to  form  water,  whilst  the  copper 
at  the  —  pole,  that  is,  at  the  copper  plate,  is  separated  in  the 
metallic  form. 

A  highly  interesting  application  has  been  made  of  this  metallic 
precipitate  of  copper,  and  is  known  under  the  name  of  galvano- 
plastics  (electrotype) ;  it  is  only  necessary  to  give  a  definite  form 
to  the  —  elements  of  a  combination  of  this  kind,  to  obtain  im- 
pressions of  this  form  in  metallic  copper. 

It  is  necessary  to  modify  somewhat  the  form  of  the  Becquerel 
circuit  before  applying  it  for  this  purpose.  The  apparatus  repre- 
sented in  Fig.  415,  is  especially  well  adapted  for  the  multiplication 
of  coins,  medals,  &c. ;  a  b  is  a  glass  vessel  open  at  the  top,  about 
6-8  inches  in  diameter.  Within  this  hangs  a  second  narrower 
glass  vessel  c  d,  likewise  opening  at  the  top,  but  closed  at  the 

36* 


426 


CHEMICAL    ACTIONS    OF    THE    VOLTAIC    PILE. 


bottom  by  having  a  bladder  tied  to  it.  Somewhat  above  the  mid- 
Fig.  415.  die,  a  wire  is  tightly  bound  round  the 
inner  vessel,  which  it  lifts  up  in  such 
a  manner,  that  the  bladder  is  raised 
from  1,5  to  2  inches  above  the  bot- 
tom, the  wire  branching  out  in  three 
arms,  which  are  attached  to  the  rim 
of  the  outer  vessel.  The  inner  vessel 
is  filled  with  very  dilute  sulphuric 
acid,  while  the  space  intervening 
between  the  inner  and  outer  cylin- 
der is  filled  with  a  solution  of 

sulphate  of  copper.  Two  pieces  of  wood  laid  cross-ways  sup- 
port in  the  sulphuric  acid  a  zinc  block,  to  which  a  copper  wire  is 
soldered,  connecting  the  zinc  block  with  the  mercury-cup  q.  A 
second  copper  wire  passes  from  this  cup  to  the  form  lying  in  the 
solution  of  sulphate  of  copper,  which,  of  course,  must  be  made  of 
a  substance  more  electro-negative  than  zinc. 

Such  a  form  may  be  procured  by  taking  an  impression  of  a 
coin  with  Rose's  fusible  metal,  and  still  more  easily  by  means  of 
wax  or  stearine.  These  two  substances  must  be  fused  together 
with  finely  pulverized  graphite,  and  the  liquid  then  poured  on  the 
metal,  which  must  be  protected  by  a  rim  of  paper,  when  a  very 
beautiful  form  is  obtained. 

This  matrix,  however,  is  not  a  conductor,  and  only  becomes  so 
by  covering  the  surface,  which  is  to  receive  the  copper,  with  a 
thin  delicate  layer  of  fine  copper  bronze.  This  coating,  which 
may  be  laid  on  with  a  fine  brush,  does  not  in  any  way  take  from 
the  purity  and  sharpness  of  the  outlines.  The  matrix  must  be 
plunged  into  the  solution  with  its  conducting  surface  turned  up- 
ward. The  copper  wire  requires  only  to  be  in  contact  with  the 
fine  graphite  layer. 

The  portion  of  the  copper  wire  plunged  in  the  solution  of  sul- 
phate of  copper  must  be  covered  with  shell-lac,  or  sealing-wax, 
to  prevent  metallic  copper  from  being  deposited  upon  this  wire, 
which-  deposition  must  be  prevented  except  where  it  is  attached 
to  the  matrix. 

The  current  circulating  through  the  apparatus  is  very  weak ; 
the  copper  deposits  itself  slowly  upon  the  copper  surface,  and 
subsequently  upon  the  copper  wire;  it  is,  therefore,  necessary 


CHEMICAL    ACTIONS    OF    THE   VOLTAIC    PILE. 


427 


from  time  to  time  to  place  the  wire  at  a  different  part  of  the 
mould.  The  layer  of  copper  will  be  thick  enough,  and  may  be 
removed  in  one  or  more  days,  according  to  the  strength  of  the 
current.  The  copper  deposit  is  most  regular  with  a  weak  current, 
on  which  account  the  fluid,  in  which  the  zinc  block  is  plunged, 
should  be  only  slightly  acid. 

The  solution  of  sulphate  of  copper  becomes  lighter  in  color 
in  proportion  to  the  copper  deposited  from  it.  It  is  necessary 
occasionally  to  renew  the  solution  as  it  becomes  exhausted. 

It  is  often  better  to  place  the  solution  of  sulphate  of  copper 
with  the  mould  in  the  inner  vessel,  and  the  acid  with  the  zinc 
block  in  the  outer  vessel. 

[A  very  neat  decomposition  cell  consists  of  a  box  a  foot  deep, 
a  foot  long,  and  a  few  inches  wide.  Two  parallel  wires  are  ex- 
tended along  the  top,  one  connected  with  the  negative,  and  the 
other  with  the  positive  metal  of  the  battery.  On  the  former  are 
hung  the  moulds,  and  on  the  latter,  a  sheet  of  copper.  Fig.  416 
represents  one  of  these  cells  connected  with  a  Smee's  battery. 

Fig.  416. 


This  latter  consists  of  platinized  silver  and  amalgamated  zinc. 
There  is  no  diaphragm,  and  the  exciting  liquid  is  acid  and  water. 
The  silver  plate  to  be  connected  with  the  copper  in  the  decom- 
position cell,  and  the  zinc  with  the  moulds. 

A  full  account  of  the  various  processes  employed  in  electrotype 
will  be  found  in  a  little  work  on  Electrotype  Manipulations,  by 
C.  V.  Walker.— (Carey  and  Hart.)] 

Many  important  applications  of  galvano-plasticshave  been  made 
within  the  last  few  years;  by  this  means  impressions  of  woodcuts 
have  been  taken,  which  retain  all  the  purity  and  sharpness  of  the 
original  outlines,  and  thus,  as  many  fac-similes  as  we  like  may 


428  CHEMICAL    ACTIONS    OF    THE    VOLTAIC    PILE. 

be  taken  of  the  original,  without  any  difference  being  perceptible 
between  the  first  and  last  impressions.  The  woodcuts  of  the 
original  German  edition  of  this  work,  from  which  those  in  our 
present  translation  are  copied,  were  impressed  by  copper  type  of 
this  description.  A  graved  copper  plate  will  not  bear  many  im- 
pressions being  taken  of  it,  without  manifesting  a  decided  dete- 
rioration in  the  latter  impressions.  Hence,  the  value  of  the  proof- 
impression,  and  hence,  the  reason  that  steel  engraving  is  so  much 
valued,  for  a  steel  plate  will  bear  a  much  larger  number  of  im- 
pressions being  taken  of  it.  Steel,  however,  offers  decided  dis- 
advantages with  reference  to  art,  for  owing  to  the  hardness  of  its 
texture  it  opposes  great  difficulties  to  the  artist,  who  cannot  pos- 
sibly complete  as  perfect  a  work  on  steel  as  on  copper.  Now, 
however,  a  means  has  been  devised  of  multiplying  copper  plates, 
even  when  of  a  large  size,  by  the  galvano-plastic  process,  so  that 
the  impressions  of  the  copies,  of  which  we  may  have  an  unlimited 
number,  are  quite  equal  to  the  original  plates. 

Kobell,  of  Munich,  has  proposed  a  method  by  which  pictures, 
drawn  in  bistre  or  Indian  ink,  may  be  multiplied  by  galvano 
plastically.  A  copper  plate  silvered  over  is  used  for  painting  on, 
and  the  color  prepared  for  the  purpose,  is  an  ochre  or  coke  rubbed 
up  in  a  solution  of  wax  and  oil  of  turpentine,  adding  a  little  Dam- 
mara  varnish.  This  color  is  laid  on  the  plate  in  such  a  way,  that 
the  brightest  lights  remain  free,  the  paint  being  laid  on  thicker  in 
proportion  to  the  depth  of  shadow  required.  As  soon  as  the  picture 
is  finished,  a  wash  of  finely  pulverized  graphite  is  laid  on  with 
a  fine  brush,  and  the  plate  is  put  into  the  galvano-plastic  appara- 
tus. By  degrees,  the  copper  is  precipitated  upon  the  painted 
plate,  forming  a  second  copper  plate,  on  which  all  the  lights  ap- 
pear smooth,  and  the  shadows  are  deeply  impressed ;  this  plate 
will  now  yield,  if  treated  like  a  graved  copper  plate,  impressions 
similar  to  an  Indian  ink  drawing.  Thayer,  of  Vienna,  has 
brought  this  method  to  great  perfection,  and  there  is  reason  to 
expect  that  it  will  prove  of  still  greater  practical  importance  to 
art. 

In  the  same  manner  as  copper  is  precipitated  at  the  negative 
pole  of  the  circuit,  by  a  galvanic  process  from  a  solution  of  sul- 
phate of  copper,  other  metals,  as  gold,  silver,  platinum,  &c.,  are 
deposited  at  the  negative  pole  from  suitable  solutions,  and  we 
may  thus  gild  and  silver  other  metals,  &c.  It  would  lead  us 


CHEMICAL    ACTIONS    OF    THE    VOLTAIC    PILE.  429 

beyond  our  proper  limits  were  we  to  enlarge  further  upon  this 
subject. 

An  interesting  illustration  of  metallic  precipitations  is  presented 
by  the  NobilVs  colored  rings.  If  we  pour  a  few  drops  of  a  solu- 
tion of  acetate  of  lead  upon  a  silver  plate,  and  then  touch  the 
silver  in  the  middle  of  the  fluid  with  a  small  piece  of  zinc,  several 
concentric  colored  rings  will  be  formed  around  the  places  of 
contact.  These  rings  appear  still  more  beautiful  on  putting  the 
fluid  between  the  poles  of  a  pile  composed  of  many  plates,  flatten- 
ing the  one  pole,  and  pointing  the  other,  and  then  turning  the 
latter  in  such  a  manner  to  the  former,  that  the  electric  current 
passes  through  the  fluid  from  the  flattened  to  the  pointed  pole,  or 
vice  versa.  Nobili  obtained  similar  phenomena  of  colors  with 
other  fluids. 

Chlorides,  iodides,  and  bromides  of  metals  are  simply  decom- 
posed by  the  electric  current,  the  metal  being  deposited  at  the 
negative,  and  the  chlorine,  iodine,  and  bromine  at  the  positive 
pole.  The  weakest  current  is  capable  of  decomposing  iodide  of 
potassium. 

On  exposing  aqueous  solutions  to  the  action  of  the  electric  cur- 
rent, the  result  of  the  decomposition  will  often  be  modified  by  the 
presence  of  the  water.  To  avoid  this,  Faraday  has  reduced  many 
bodies  to  a  fluid  state  by  fusion,  and  thus  exposed  them  to  the 
action  of  the  current.  He  thus  decomposes  chloride  of  lead,  chlo- 
ride of  silver,  &c.,  laying  them  upon  a  glass  plate,  and  fusing 
them  over  a  spirit  lamp,  and  then  immersing  both  polar  wires  into 
the  fluid  mass.  If  polar  wires  of  silver  were  plunged  in  fluid 
chloride  of  silver,  the  silver  would  be  deposited  at  the  —  pole, 
which  had  attached  itself  to  the  wire,  whilst  the  other  silver  wire 
would  be  dissolved  by  the  liberated  chlorine. 

We  have  hitherto  only  spoken  of  decompositions  produced  by 
the  galvanic  current,  but  this  current  also  favors  to  chemical 
combinations.  If  we  bring  any  easily  oxidizable  metal,  as  zinc, 
for  instance,  near  the  -f  polar  wire,  the  metal  will  very  easily 
combine  with  the  oxygen  separated  from  the  water ;  zinc  only 
dissolves  slowly  in  diluted  sulphuric  acid,  if  it  be  quite  chemically 
pure  ;  on  touching  it  with  a  piece  of  silver,  a  marked  development 
of  gas  instantly  begins  to  take  place  at  the  silver,  while  the  zinc 
combines  with  the  oxygen  to  form  oxide,  which  is  dissolved  by 
the  acid. 


430  CHEMICAL    ACTIONS    OF    THE   VOLTAIC    PILE. 

If  the  polar  wires  of  a  galvanic  battery  be  made  of  zinc,  and 
then  immersed  in  acidulated  water,  the  decomposition  of  the 
water  will  go  on  precisely  as  if  platinum  or  copper  wires  were 
used.  The  hydrogen  gas  will  be  separated  at  the  wire  of  the 
negative  pole,  which  will  not  be  affected  by  the  acid,  as  would 
otherwise  be  the  case  if  it  were  not  made  negatively  electric  by 
its  connection  with  the  pile,  and  thus  protected  from  oxidation ; 
the  wire  of  the  polatine  pole,  on  the  contrary,  will  be  so  much  the 
more  rapidly  acted  upon. 

A  metal,  affected  by  an  acid,  or  any  other  fluid,  can  be  pro- 
tected from  oxidation  by  being  brought  into  connection  with  a 
metal  positively  electrified,  so  as  to  form  the  —  pole  of  a  simple 
circuit. 

Whilst  the  current  arising  from  the  contact  of  two  metals 
plunged  in  the  same  fluid  increases  the  affinity  of  one  of  these 
for  one  element  of  the  fluid,  the  power  of  the  other  metal  to  un- 
dergo the  same  changes  is  proportionally  diminished.  Thus, 
when  a  zinc  and  a  copper  plate,  come  into  contact  in  a  dilute 
acid,  the  zinc  will  oxidize  more  rapidly,  and  the  copper  less  than 
would  otherwise  be  the  case.  Davy^s  experiments,  on  the  pre- 
servation of  the  coppering  of  ships,  affords  a  beautiful  illustration 
of  this  principle.  A  copper  plate,  when  immersed  in  sea  water, 
is  exposed  to  a  rapid  oxidation ;  but,  if  the  copper  be  brought 
into  contact  with  zinc  or  iron,  these  metals  will  be  dissolved,  and 
the  copper  thus  protected.  Davy  has  ascertained  that  a  piece  of 
zinc  of  the  size  of  the  head  of  a  small  nail  is  sufficient  to  protect 
40  to  50  square  inches  of  copper. 

It  has  unfortunately  been  shown,  however,  that  this  excellent 
mode  of  preserving  copper  cannot  be  practically  made  use  of,  as 
copper  must  be  acted  upon  to  a  certain  extent,  in  order  to  save  it 
from  being  injured  by  the  adhesion  of  sea-weed  and  marine 
animals. 

The  same  principle  has  been  applied  by  Von  Althaus  to  prevent 
the  rusting  of  the  iron  pans  used  in  evaporating  brine.  Here, 
however,  the  protecting  zinc  could  not  be  applied  to  the  pans 
themselves,  as  the  sulphate  of  zinc  would  distribute  itself  through 
the  brine,  he,  therefore,  separated  the  corners  of  the  pans  by  a 
board,  and  filled  these  spaces  with  zinc,  whose  bottoms  were 
formed  with  iron  plates.  Thus  the  zinc  is  in  metallic  connection 
with  the  iron,  and  the  fluid  passes  in  sufficient  quantity  through 


THE    ELECTRO-CHEMICAL    THEORY.  431 

the  wood  to  the  zinc  to  complete  the  circuit,  while  the  sulphate  of 
zinc  engendered  cannot  destroy  the  purity  of  the  solution  of  salt. 

By  this  means,  evaporation  was  effected  at  a  lower  temperature, 
and  a  considerable  saving  made  in  the  expenditure  of  fuel. 

The  Electro- Chemical  Theory. — The  hitherto  described  phe- 
nomena exhibit  remarkable  relations  between  chemical  and  elec- 
trical forces.  It  had  already  been  vaguely  conjectured,  that 
electrical  forces  were  concerned  in  chemical  phenomena ;  this 
view  was,  however,  only  confirmed  when  the  decomposition  of 
water  was  effected  by  the  voltaic  battery ;  that  is  to  say,  it  was 
reserved  for  Davy  and  Berzelius  to  develop  these  views ;  and  they 
established  the  electro-chemical  theory,  according  to  which,  we 
must  seek  for  the  fundamental  cause  of  chemical  combinations  in 
electric  attraction.  Although  it  may  not  be  fully  proved,  that 
chemical  affinity  and  electrical  attraction  are  perfectly  identical, 
it  must  be  confessed,  that  this  theory  combines  many  facts  into 
one  connecting  bond  in  a  manner  that  cannot  be  refuted  by  ex- 
perience. 

As  zinc  and  copper,  when  brought  into  contact  with  each  other 
become  oppositely  electric,  so,  also,  according  to  the  electro- 
chemical theory,  the  atoms  of  every  two  elements  become  oppo- 
sitely electric  when  brought  into  contact  with  each  other;  in 
short,  all  elements  are,  according  to  the  signification  already 
given  at  page  406,  members  of  the  series  of  tension.  The 
extremes  of  this  perfectly  complete  series  are  oxygen  and  potas- 
sium, the  former  being  the  — ,  and  the  latter  the  +  extremity. 
The  following  is  the  complete  series  of  tension. 


Oxygen  Bromine 

Sulphur  Iodine 

Selenium  Fluorine 

Tellurium  Phosphorus 

Nitrogen  Arsenic 

Chlorine  Carbon 

Chromium  Cerium 

Molybdenum  Lanthenium 

Borax  Yttrium 

Vanadium  Cobalt 

Tungsten  Nickel 

Antimony  Iron 


432  THE    ELECTRO-CHEMICAL    THEORY. 

Tantalium  Cadmium 

Titanium  Zinc 

Silicium  Hydrogen 

Osmium  Manganese 

Gold  Zirconium 

Iridium  Aluminum 

Rhodium  Thorine 

Platinum  Beryllium 

Palladium  Magnesium 

Mercury  Calcium 

Silver  Strontium 

Copper  Barium 

Uranium  Lithium 

Bismuth  Sodium 

Lead  Potassium 

+ 

This  series  contains  all  the  simple  substances,  and  to  each  its 
place  is  assigned,  although  there  is  still  much  uncertainty  in  this 
respect,  and  the  position  of  most  bodies,  in  the  series  of  tension, 
is  only  approximatively,  but  not  accurately,  determined.  This 
position  has  only  been  ascertained  by  direct  experiment  for  a 
very  few  bodies ;  the  place  of  the  majority  having  been  conjec- 
tured from  their  chemical  relation. 

According  to  the  electro-chemical  theory,  the  atoms  of  the  ele- 
ments are  not  electrical  in  themselves,  but  become  so  on  being 
brought  into  contact  with  others,  whence  it  happens  that  the 
same  body  may  at  one  time  be  +,  and  at  another  —  electric. 
Thus,  for  instance,  sulphur  in  combination  with  oxygen  is  the 
electro-positive,  and  in  conjunction  with  hydrogen  the  electro- 
negative, element. 

We  have  seen,  that  two  heterogeneous  metal  plates,  brought 
into  contact  with  each  other,  become  oppositely  electric;  but, 
that  the  greatest  part  of  the  electricity  developed,  remains  com- 
bined on  the  surface  of  contact;  the  same  is  the  case  with  chemi- 
cal combinations.  If,  for  instance,  a  particle  of  oxygen  and  one 
of  hydrogen  come  into  contact,  the  former  will  become  — ,  and  the 
latter  +  electric,  both  electricities  will  attract  each  other,  and 
combine  almost  perfectly,  owing  to  their  close  approximation. 
If,  however,  there  is  a  little  free  +  electricity  on  the  one  particle, 
and  —  electricity  on  the  other,  the  chemical  combination  cannot 


THE    ELECTROLYTIC    LAW.  433 

give  any  evidence  of  free  electricity,  owing  to  the  -f  and  —  par- 
ticles being  uniformly  distributed;  thus,  whenever  we  lay  our 
hands  on  the  body,  an  equal  number  of  +  and  —  electric  parti- 
cles will  be  touched. 

In  the  first  place,  the  simple  substances  combine  to  form  binary 
compounds.  The  compound  bodies,  as  the  oxygen,  sulphur,  and 
chlorine  combinations,  exhibit,  among  themselves,  a  relation  simi- 
lar to  that  of  simple  substances;  these  binary  combinations  of  the 
simple  elements,  oxides,  sulphurets,  and  chlorides,  &c.,  which  are 
characterized  by  negatively  electric  properties,  and,  at  the  same 
time,  capable  of  entering  into  combinations  of  a  higher  order,  are 
termed  acids;  while  those  constituting  the  part  of  the  positively 
electric  constituents,  are  called  salifiable  bases. 

The  character  of  an  acid  is  generally  the  more  strongly  ex- 
pressed in  proportion  to  the  contiguity  of  its  elements  to  the 
negative  end  of  the  scale  of  tension ;  hence,  sulphuric  acid  is  the 
strongest  of  all  acids.  Oxygen  forms  acids  in  connection  with 
the  bodies  standing  at  the  head  of  the  above  series,  and  bases 
with  the  elements  at  the  positive  end;  thus,  potassium  is  the 
strongest  of  all  bases. 

When  the  same  body  combines  in  several  different  proportions 
with  oxygen,  the  combination  will  be  so  much  the  more  negatively 
electric,  because  it  will  assume  more  of  the  acid,  and  less  of  the 
properties  of  a  base,  in  proportion  as  the  electro-negative  element, 
the  oxygen,  predominates.  Thus,  1  equivalent  of  manganese 
combined  with  1  equivalent  of  oxygen,  forms  oxide  of  manganese, 
which  possesses  the  properties  of  a  base,  whilst  1  equivalent  of 
manganese  -f  3  equivalents  oxygen,  forms  manganic  acid. 

The  electro-chemical  theory  does  not,  in  its  present  limits, 
embrace  an  explanation  of  all  chemical  phenomena;  but  the 
classification  of  bodies,  founded  upon  it,  agrees  sufficiently  with 
their  relations,  so  as  to  give  a  clear  insight  into  chemical  laws. 

The  Electrolytic  Law.— No  electric  current,  or  comparatively 
only  a  very  weak  one,  can  pass  through  a  fluid  without  its  passage 
being  attended  by  chemical  decomposition.  Such  a  decomposi- 
tion as  this  occurs  in  every  cell  of  every  galvanic  apparatus,  as 
long  as  the  circuit  remains  complete,  and  Faraday  has  shown  that 
the  quantity  of  the  electric  current  is  proportional  to  the  decom- 
position taking  place  in  each  individual  cell. 

It  cannot  be  denied,  that  an  intimate  relation  exists  between 
37 


434  THE   ELECTROLYTIC   LAW. 

the  passage  of  the  electric  current,  through  fluids,  and  their  de- 
composition ;  and,  it  may  even  be  asserted,  that  the  passage  of  the 
electricity  is  effected  by  chemical  decomposition.  The  positive 
current  passes  in  every  cell,  from  the  zinc,  through  the  fluid,  to 
the  copper;  but  the  particles  of  the  hydrogen  pass  in  the  same 
direction ;  they  are  the  conductors  of  the  -f  electricity,  which  is 
conveyed  by  them  to  the  copper  plate.  Indeed,  we  have  seen, 
that,  in  accordance  with  the  principles  of  the  electro-chemical 
theory,  the  elements  are  held  firmly  together  in  each  atom  of 
water,  because  oxygen  and  hydrogen,  brought  into  contact,  be- 
come oppositely  electric,  and  because  these  opposite  electricities 
of  the  elements  of  water  mutually  combine  with  each  other. 
When  a  particle  of  hydrogen  is  separated  from  its  oxygen,  all  its 
combined  electricity  will  be  liberated ;  it  will  be,  however,  imme- 
diately recombined  when  the  hydrogen,  on  the  other  hand,  com- 
bines with  another  particle  of  oxygen,  and  thus  each  atom  of 
hydrogen  will  carry  off  its  combined  -f  electricity,  whilst,  at  the 
same  time,  its  positive  electricity  will  be  liberated  at  the  —  pole 
with  the  hydrogen. 

Whilst  the  ordinary  zinc  of  commerce  is  rapidly  dissolved  when 
plunged  into  dilute  sulphuric  acid,  chemically  pure  zinc,  or  amal- 
gamated zinc,  will  remain  unaffected  in  the  same  fluid.  If  we 
construct  a  galvanic  circuit  with  chemically  pure,  or  amalga- 
mated zinc  plates,  no  decomposition  can  possibly  occur  in  such  a 
circuit  while  open.  But  the  moment  it  is  closed,  a  decomposition 
of  water  begins  in  every  cell ;  there  is,  however,  no  more  water 
decomposed,  nor  zinc  dissolved,  than  is  necessary  to  conduct  the 
circulating  current ;  the  quantity  of  the  dissolved  zinc  must,  there- 
fore, stand  in  a  definite  relation  to  this  current.  Faraday  made 
use  of  the  current  of  such  a  circuit  for  the  decomposition  of  water, 
and  ascertained  definitively  the  amount  of  explosive  gas  evolved 
in  a  given  time.  It  was  thus  found  that,  for  each  equal  portion 
of  hydrogen  gas  liberated  between  the  polar  wires,  or,  rather,  the 
plates  of  the  poles,  32,3  equal  portions  of  zinc  were  dissolved  in 
each  cell.  But  now  the  weights  of  the  chemical  equivalents  of 
hydrogen  and  zinc  are  to  each  other  as  12,48  to  403,23,  or  as  1 
to  32,3.  For  every  equivalent  of  hydrogen,  therefore,  evolved  in 
the  decomposing  cells,  1  equivalent  of  zinc  must  be  dissolved  in 
each  cell  of  the  circuit. 

If  the  same  current  be  conducted  through  4  decomposing  cells, 


THEORY   OF   CONSTANT    CIRCUITS.  435 

of  which  the  first  contains  water,  the  second  chloride  of  silver,  the 
third  chloride  of  lead,  the  fourth  chloride  of  tin,  all  in  a  fluid 
condition,  the  quantities  of  hydrogen  gas,  silver,  lead,  and  tin, 
which  are  precipitated  at  the  four  —  poles,  are,  to  each  other,  as 
1  :  108  :  103,6  :  57,9,  whilst,  at  the  +  poles,  oxygen  and  chlorine 
are  separated  in  the  proportions  of  8 :  35,4.  Similar  facts  have 
been  demonstrated  for  many  other  composite  bodies. 

It  follows,  from  these  facts,  that  the  chemical  equivalents  repre- 
sent those  relative  weights  of  the  substances  which  assume  an 
equally  strong  electric  polarity  in  connection  with  one  and  the 
same  element. 

Theory  of  Constant  Circuits. — The  common  voltaic  circuit,  in 
which  only  one  fluid  is  used,  gives,  as  we  have  already  seen,  an 
uncommonly  strong  current  at  the  first  moment ;  this,  however, 
soon  abates  in  intensity,  whilst,  in  the  Becquerel  circuits,  Daniel's, 
Groves',  and  Bunsen's  apparatus,  the  current  continues  with  un- 
abated force.  Now  that  we  have  learnt  to  understand  the  chemi- 
cal phenomena  in  the  circuit,  we  may  be  able  to  explain  why  the 
current  remains  constant  in  the  one  kind  of  apparatus,  and  loses 
rapidly  its  intensity  in  the  other. 

A  zinc  and  a  copper  plate,  united  by  a  copper  wire  at  the  top, 
are  plunged  into  a  vessel  (Fig.  417)  filled  with  a  solution  of  sul- 
phate of  zinc.  At  first,  a  tolerably  strong 
current  will  be  engendered,  which,  how- 
ever, will  soon  abate,  and,  finally,  en- 
tirely cease.  The  reason  of  this  cessation 
will  be  soon  understood,  on  considering 
the  process  of  the  decomposition ;  the  inc  ^ 
oxide  of  zinc  of  the  solution  is  soon 
decomposed,  the  oxygen  attaches  itself 
to  the  zinc  plate  in  order  to  form  a  new 
oxide,  whilst,  on  the  other  side,  metallic 
zinc  is  precipitated  on  the  copper  plate ; 

after  a  time,  the  copper  plate  becomes  wholly  covered  over  with 
zinc,  when  the  current,  of  course,  ceases.  The  copper  is  now  no 
longer  in  connection  with  the  fluid,  but  there  is  zinc  on  both  sides 
of  the  copper,  and  of  the  fluid;  the  copper  becomes  negatively 
excited  where  it  is  soldered  to  the  zinc  plate,  but  this  excitement 
does  not  occasion  any  current,  since  the  newly  formed  zinc  coat- 
ing gives  rise  to  a  totally  opposite  one. 


436  THEORY    OF    CONSTANT    CIRCUITS. 

If  we  take  dilute  sulphuric  acid,  instead  of  the  solution  of  oxide 
of  zinc,  the  water  of  the  fluid,  between  the  zinc  and  copper  plate, 
will  be  decomposed ;  in  the  place  of  the  zinc,  which  is  precipi- 
tated on  the  copper  plate,  as  in  the  former  case,  the  hydrogen  will 
now  be  liberated;  the  copper  plate  will  be  covered  with  a  coating 
of  hydrogen,  which  will  not,  however,  come  into  such  intimate 
connection  with  the  copper  as  in  the  former  case,  and  cannot, 
therefore,  so  completely  prevent  the  fluid  from  coming  into  con- 
tact with  the  copper  plate  as  in  the  other.  A  total  cessation  of 
the  current  is,  therefore,  not  possible  here ;  but  the  separation  of 
hydrogen  (which,  according  to  Buff's  experiments  on  the  scale 
of  tension,  stands  below  zinc),  occasions  a  diminution  of  the 
intensity  of  the  current,  in  the  same  way  as,  in  the  other  case, 
the  deposition  of  zinc  had  done. 

If  the  reason  of  the  diminution  of  the  current  in  ordinary  cir- 
cuits be  rightly  understood,  it  will  be  easy  to  find  a  method  of 
avoiding  this'  occurrence ;  it  being  only  necessary  to  devise  some 
arrangement  by  which  the  separation  of  hydrogen  on  the  copper 
and  platinum  plates  may  be  prevented,  so  that  these  plates  may 
always  remain  in  contact  with  the  fluid  in  the  same  manner. 

In  BecquerePs  and  Daniel's  circuit,  metallic  copper  is  deposited 
on  the  copper  plates  instead  of  hydrogen,  and  thus  a  pure  copper 
surface  is  always  left  in  contact  with  the  fluid.  In  Groves'  battery, 
the  platinum  is  surrounded  by  a  layer  of  nitric  acid,  which  like- 
wise circulates  round  the  charcoal  in  Bunsen's  apparatus ;  this 
acid  prevents  the  separation  of  the  hydrogen  on  the  platinum  or 
the  charcoal,  for,  at  the  moment  of  their  origin,  the  deposited 
particles  of  hydrogen  are  again  oxidized,  and  nitrous  acid 
formed. 

This  seems  to  be  the  most  suitable  place  to  say  a  few  words  con- 
cerning the  various  theories  that  have  been  advanced  in  explana- 
tion of  the  electrical  phenomena  of  galvanic  batteries,  as  they  have 
formed  the  subject  of  the  most  animated  discussions  between 
different  scientific  men. 

The  oldest  of  these  is  the  theory  of  contact,  established  by 
Volta,  according  to  which,  the  contact  of  different  metals  is  the 
only  source  of  the  electricity  of  the  pile.  Volta  had  devoted 
especial  attention  to  the  study  of  the  actions  of  tension  in  bat- 
teries, and  these  are  explained  more  satisfactorily,  according  to 
his  theory,  than  to  that  of  any  other.  He  doubtlessly  disregarded 


THEORY   OF   CONSTANT   CIRCUITS.  437 

chemical  phenomena,  from  being  wholly  ignorant  of,  or  but 
slightly  acquainted  with  them,  and  hence  it  arises  that  he  did  not 
devote  sufficient  attention  to  the  part  played  by  the  fluids  in  the 
circuit,  considering  them  merely  as  conductors,  and  not  as  elec- 
tromotors. 

When  the  chemical  actions  of  the  battery  were  better  known 
and  more  accurately  observed,  the  voltaic  theory  of  contact  was 
not  satisfactory,  and  it  became  necessary  either  to  corroborate 
and  enlarge  upon  it,  in  order  to  admit  of  its  embracing  the 
newly  discovered  facts,  or  to  set  it  wholly  aside,  and  to  form  an 
entirely  new  hypothesis.  Both  methods  have  been  adopted,  and 
that  by  distinguished  natural  philosophers. 

The  opponents  of  the  theory  of  contact,  among  whom  Faraday 
must  be  specially  noticed,  consider  the  chemical  action  exerted 
by  the  fluid  upon  the  metal,  as  the  source  of  the  electric  current 
of  the  circuit. 

Faraday  was  likewise  induced,  by  his  theoretical  views,  to  in- 
troduce a  new  nomenclature,  calling  the  poles  "Electrodes,"  or 
the  courses  pursued  by  the  electric  current  in  entering  the  decom- 
posing fluid,  the  positive  pole  "  Anode,"  and  the  negative  pole 
"  Cathode."  The  constituents  of  the  electrolyte  (the  decomposed 
body)  are,  according  to  his  nomenclature,  Ions,  the  Cathion  being 
the  element  separated  at  the  cathode,  and  the  Jlnion  that  which  is 
found  at  the  anode. 

It  will  not  surprise  us  that  so  much  misconception  and  differ- 
ence of  opinion  should  exist  with  respect  to  the  source  of  the 
electricity  in  the  circuit,  when  we  consider  how  little  is  known  to 
us  of  the  actual  nature  of  electricity.  What  do  we  know  con- 
cerning the  generation  of  electricity  by  friction,  beyond  the  simple 
fact?  The  reason  of  the  difference  of  opinion  that  existed  regard- 
ing galvanism,  evidently  arose  from  Volta?s  disregard  of  the 
influence  exercised  by  chemistry.  This  deficiency,  or,  rather,  the 
partiality  of  this  view,  could  not  long  escape  observation;  but 
while  many  learned  men  were  striving  to  point  out  the  importance 
of  this  influence,  they  fell  into  the  opposite  extreme  of  ascribing 
every  effect  to  chemistry,  and  neglected  those  well  proved  facts 
which  constituted  the  basis  of  the  theory  of  contact.  Some  even 
suffered  themselves  to  be  so  far  led  astray  as  to  question  the 
correctness  of  Voltcts  fundamental  experiments,  or  explained 

37* 


438      MAGNETIC   ACTIONS   OF   THE   GALVANIC   CURRENTS. 

them  by  the  hypothesis  that  the  precious  metals  underwent  oxi- 
dation. 

The  adherents  of  both  theories  were  most  zealously  active  in 
advancing  proofs  of  the  correctness  of  their  own  opinions,  and  to 
these  efforts  we  are  principally  indebted  for  the  advance  that  has 
been  made  in  the  science  of  galvanism.  Fechner,  above  all, 
deserves  praise  for  having  established,  beyond  doubt,  the  cor- 
rectness of  Volta's  fundamental  experiments,  and  thus  justified 
the  views  concerning  the  excitement  of  electricity  in  various 
metals.  Faraday,  on  his  side,  has  shown  that  galvanic  currents 
may  be  produced  without  the  contact  of  heterogeneous  metals ; 
that  the  chemical  decomposition  of  the  fluid  of  the  pile  is  propor- 
tional to  the  quantity  of  the  electrical  current ;  and  that,  conse- 
quently, this  decomposition  stands  in  the  closest  connection  with 
the  formation  of  the  current  in  the  hydro-electric  circuit. 

As  a  theory  of  galvanism  should,  if  possible,  embrace  all  the 
phenomena  of  the  circuit,  we  can  scarcely  look  for  truth  in  the 
extreme  views  of  either  party.  It  seems,  therefore,  most  suitable 
to  the  present  stage  of  science  to  adopt  some  modified  theory  of 
contact  as  given  above,  since  by  this  means  we  shall  be  best  able 
to  consider  from  one  common  point  of  view  the  different  phe- 
nomena exhibited  in  the  circuit. 

Magnetic  Actions  of  the  Galvanic  Current. — It  had  long  been 
known,  that,  under  certain  circumstances,  powerful  electric 
charges  could  affect  the  magnetic  needle;  it  had,  for  instance, 
been  observed,  that  the  needle  of  the  compass  lost  the  property 
of  directing  the  course  of  the  ship,  if  the  latter  had  been  struck 
by  lightning.  Many  natural  philosophers  attempted  to  produce 
similar  phenomena  by  the  discharge  of  Leyden  jars,  and,  indeed, 
some  succeeded  in  altering  the  magnetic  condition  of  very  small 
needles,  either  by  suffering  the  spark  to  pass  very  near  the  needle, 
or  the  whole  force  of  the  discharge  to  pass  immediately  through  it. 
But  all  these  experiments  yielded  no  regular  results,  and  people 
remained  satisfied  with  the  view  that  the  electric  shock  acted  upon 
the  magnetic  needle  as  the  stroke  of  a  hammer.  Subsequent  ex- 
periments were  made  in  galvanic  electricity  which  yielded  no 
better  fruit;  finally,  in  the  year  1820,  Oersted,  professor  at  the 
University  of  Copenhagen,  discovered  a  means  of  causing  elec- 
tricity to  act  certainly  and  constantly  upon  a  magnet.  He  thus 
opened  to  the  scientific  men  of  all  countries  a  new  and  extended 


MAGNETIC    ACTIONS    OF    THE    GALVANIC    CURRENTS.      439 

field  of  investigation,  and  never  before,  perhaps,  had  science  been 
enriched  in  a  short  time  with  the  acquisition  of  so  many  new 
truths. 

Electricity  must  be  in  motion  to  act  upon  magnetism  when  at 
rest,  and  in  a  state  of  great  tension,  it  does  not  affect  the  magnet, 
as  does  a  continuous  electric  current. 

In  fact,  on  bringing  a  freely  suspended  magnetic  needle  to  the 
terminating  wire  of  a  pile  while  the  electric  current  is  passing, 
the  needle  will  deviate.  This  was  the  first  experiment  made  by 
Oersted,  and  it  is  singular  that  a  similar  observation  had  not  long 
since  been  accidentally  made  in  the  many  experiments  tried  with 
the  pile. 

The  principal  experiment  on  the  action  of  the  galvanic  current 
upon  the  needle  may  be  made  in  the  following  manner:  a  some- 
what thick  copper  wire  must  be  bent  into  a  square,  the  sides  of 
which  must  be  from  8  to  10  inches  in  length ;  we  must  now 
plunge  the  two  extremities  of  the  wire  a  b  andfg,  Fig.  418,  into 
the  mercury  cup  of  a  galvanic  battery  of  large  surface,  (as,  for 
instance,  into  the  cup  of  the  apparatus  seen  in  Figs.  401  and 
402),  or  we  must  connect  them  with  the  poles  of 
the  Bunsen  apparatus,  securing  them  in  such  a  ^__ 
manner  that  the  planes  of  the  square  may  coin- 
cide with  the  planes  of  the  magnetic  meridian. 
If  we  assume  that  the  wire  end  a  b  is  plunged 
into  the  .positively  electric  mercury  cup,  the  cur- 
rent will  circulate  in  the  manner  indicated  by  the 
arrows.  It  will  ascend  from  b  to  c,  but  from  c  to 
d  it  will  run  in  the  direction  of  the  magnetic  me- 
ridian horizontally  from  south  to  north,  thence  will  descend  from 
d  to  e,  and  move  again  in  a  horizontal  line  from  north  to  south 
along  the  portion  of  wire  ef. 

On  holding  a  magnetic  needle  exactly  over  the  portion  of  wire 
c  d,  it  would  remain  parallel  with  the  wire  c  d,  if  no  action  of  the 
current  affected  it ;  but  the  current  makes  the  needle  deviate  in 
such  a  manner  that  the  south  pole  (that  is,  the  one  directed  towards 
the  north)  lies  to  the  east  of  the  magnetic  meridian.  If  we  hold 
the  needle  under  the  portion  of  wire  c  d,  the  end  of  the  needle 
turned  to  the  north  will  be  inclined  towards  the  west. 

The  exactly  opposite  action  is  observed  in  the  portion  of  wire 
ef,  in  which  the  current  moves  in  a  direction  parallel,  but  oppo- 


440     MAGNETIC    ACTIONS    OF    THE    GALVANIC    CURRENTS. 

site  to  that  of  the  current  in  c  d ;  when  the  needle  is  held  exactly 
over  ef,  a  deviation  to  the  west,  and  when  held  below  it,  a  de- 
viation to  the  east,  will  be  observed. 

At  first  great  difficulty  was  experienced  in  knowing  how  to 
express  in  a  few  words  the  relations  between  the  direction  of  the 
current  and  of  that  of  the  deviation ;  this  difficulty  has,  however, 
been  very  ingeniously  removed  by  Ampere,  who  has  given  the 
following  rule  for  ascertaining  at  all  times  the  direction  of  the 
deviation.  Suppose  a  little  figure  of  a  man  to  be  so  inserted  into 
the  wire  that  the  +  current  shall  enter  at  the  feet  and  pass  out  at 
the  head ;  if,  then,  the  face  of  the  figure  be  turned  to  the  needle, 
the  south  pole  of  the  latter  (the  north  end)  will  always  be  inclined 
towards  the  left  side. 

The  figure  lies  horizontally  on  the  piece  of  wire  c  d,  the  head 
turned  to  the  north,  and  the  feet  to  the  south.  If  the  needle  be 
held  over  the  wire,  the  figure  must  lie  on  its  back  in  order  to  have 
the  face  turned  towards  the  needle,  and  in  this  position  its  left 
side  will  be  the  east.  If  the  needle  be  held  below  the  wire,  the 
figure  must  be  turned  with  its  face  downwards,  when  the  left 
side  will  be  the  west. 

In  the  piece  of  wire  efy  the  feet  of  the  figure  are  turned  to  the 
north,  and  the  head  to  the  south ;  if  it  be  laid  on  its  back,  the  left 
side  will  be  the  west,  and,  of  course,  vice  versa,  if  we  lay  it  on 
its  face. 

If  a  horizontal  current,  moving  in  the  direction  of  the  magnetic 
meridian,  were  to  act  alone  upon  the  needle,  the  latter  would  place 
itself  at  right  angles  to  the  magnetic  meridian ;  but,  besides  the 
current,  terrestrial  magnetism  comes  into  play,  and  strives  to 
bring  the  needle  back  again  into  the  meridian.  The  needle 
will,  therefore,  assume  a  middle  position  under  the  influence  of 
these  two  forces,  making  an  angle  with  the  magnetic  meridian, 
which  will  approach  more  and  more  towards  a  right  angle  in 
proportion  as  the  force  of  the  current  is  comparatively  greater 
than  the  force  of  the  terrestrial  magnetism. 

The  vertically  directed  current  in  b  c  and  in  d  e  causes  the 
needle  likewise  to  deviate,  and  the  direction  of  this  deviation  may 
also  be  found  according  to  Ampere's  rules.  Let  us  suppose  this 
figure  standing  vertically  to  be  turned  towards  the  north  end ;  this 
end  must  then  incline  to  the  left.  Here  we  must  not  forget, 


THE    MULTIPLICATOR.  441 

however,  that  the  figure  must  stand  upon  its  feet  for  an  ascending 
current,  and  on  its  head  for  a  descending  one. 

It  follows,  from  Ampere's  rule,  that  the  same  vertical  current 
either  attracts  or  repels  the  north  end  of  the  needle,  according  to 
the  side  of  the  wire  on  which  this  pole  is  placed.  In  Fig.  419, 
N  S  represents  a  horizontal  needle  seen  from  above ;  JV"  is  the 
north  end  of  the  needle,  w  a  vertical  Fi 

wire,  which  naturally  seems  con- 
tracted to  a  point,  as  seen  from  above. 
If,  now,  a  -f  current  pass  from  be- 
low upward  through  the  wire,  we 
must  suppose  the  figure  to  be  up- 
right ;  but  if  this  upright  figure  be 
turned  with  its  face  towards  JV,  and  the  pole  JVin  relation  to  this 
figure  be  turned  to  the  left,  as  the  arrow  indicates,  the  needle 
will  evidently  be  repelled  by  the  wire.  If,  however,  the  needle 
is  in  the  position  JV*'  Sf,  it  will  evidently  be  attracted  by  the 
wire. 

The  Multiplicator,  or  the  Galvanometer. — Shortly  after  Oersted 
had  made  his  important  discovery,  Schweigger  constructed  his 
multiplicator,  the  object  of  which  is  to  multiply  the  electro- 
magnetic action  of  the  current.  This  instrument  is  actually  so 
sensitive,  that  it  may  serve  to  detect  the  weakest  electric  currents. 
All  parts  of  the  current  traversing  the  elongated  parallelogram 
p  q  r  o  n,  Fig.  420,  in  the  direction  of  the  arrows,  act  in  a  similar 
way  upon  the  needle  a  b,  which  rotates  in  a 
horizontal  plane.  If  a  be  the  south  end,  and  b 
the  north  end,  the  current  will  show  a  tendency 
at  all  points  to  turn  the  needle  in  such  a  manner 
that  b  shall  project  beyond  the  plane  of  the 
figure,  whilst  a  will  retreat  behind  it.  The  lower  portion  of  wire, 
therefore,  supports  the  action  of  the  upper  in  the  same  manner  as 
does  the  current  in  the  portions  p  q  and  r  o.  A  second  current 
of  the  same  force,  moving  in  the  same  direction  round  the  needle, 
will  produce  as  great  an  effect  as  the  first,  and  thus  it  will  be  with 
a  third,  a  fourth,  &c.  A  wire,  therefore,  wound  round  a  needle, 
in  100  convolutions,  all  of  which  are  traversed  by  the  same 
current,  must  produce  an  action  of  100  times  greater  intensity 
than  one  of  a  single  convolution ;  the  current  must  not,  however, 
be  propagated  laterally  from  one  winding  to  the  other,  but  must 


442 


THE   MULTIPLICATOR. 


Fig.  421. 


Fig.  422. 


traverse  the  wire  throughout  its  whole  length,  being  carried 
actually  round  the  needle.  To  effect  this,  we  take  a  copper  wire, 
from  15  to  20  yards  in  length,  and  closely  twined  round  with 
silk,  which  is  then  wound  upon  a  wooden  or  metallic  frame.  The 
two  extremities  of  the  wires  of  the  multiplicator  must  remain  free, 
so  that  they  may  be  brought  into  contact  with  the  poles  of  the  gal- 
vanic circuit.  The  needle  is  suspended  by  a  silk  untwisted  thread, 
and  the  whole  apparatus  protected  from  currents  of  air  by  a  glass 
bell.  On  making  an  experiment  with  this,  we  place  the  frame  in 
such  a  manner  that  the  planes  of  the  circumvolutions  shall  coin- 
cide with  the  magnetic  meridian,  when  the  needle  will  likewise 
be  in  the  plane  of  the  circumvolutions  while  no  current  is  passing ; 
but,  as  soon  as  this  is  established,  the  needle  will  deviate  in  pro- 
portion to  the  intensity  of  the  current. 

Nobili  has  made  a  multiplicator  infinitely  more  delicate  than 
the  one  we  have  been  considering,  by  making  use  of  two  needles 
with  opposite  poles,  instead  of  one  needle,  as  seen  in  Fig.  421, 

and  still  better  in  Fig.  422. 
In  a  system  of  needles  of 
this  kind,  the  directing 
force  of  the  earth's  mag- 
netism is  very  inconside- 
rable, it  being  only  the 
difference  of  the  forces 

with  which  the  terrestrial  magnetism  strives  to  direct  each  needle. 
If  both  needles  were  absolutely  equal,  and  possessed  a  perfectly 
equal  amount  of  magnetism,  the  directing  force  exercised  by  the 
earth  upon  this  system  would  be  null.  But  one  of  the  needles  is 
suspended  within,  and  the  other  over  the  coils  of  wire;  both  will, 

therefore,  be  turned  towards  the  same 
side  by  the  current.  An  apparatus  of 
this  kind  is  extremely  delicate. 

To  connect  the  wires  in  a  secure 
manner,  we  must  either  pass  both 
through  a  perfectly  straight  blade  of 
straw,  or  secure  them  to  a  very  thin 
wire,  as  seen  in  Fig.  422. 

The  upper  needle  moves  in  a  circle 
divided  into  360  degrees.  The  line 
connecting  0  and  180°  is  marked  upon 


I 


Fig.  423. 


THE  TANGENT  COMPASS. 


443 


424. 


the  magnetic  meridian ;  when  there  is  no  current  passing  through 
the  convolutions,  the  needle  points  to  0°.  The  deviation  of  the 
needle  increases  with  the  increasing  force  of 
the  current ;  this  force  is  not,  however,  pro- 
portional to  the  angle  of  deviation. 

The  direction  of  the  deviation  of  the  nee- 
dle determines  the  direction  of  the  current. 

Fig.  423  represents  a  complete  galvanometer,  and  424  exhibits 
the  frame,  with  the  coils  of  the  wire,  as  seen  from  above. 

The  Tangent  Compass. — When  we  have  to  do  with  stronger 
currents,  it  is  not  necessary  to  use  an  astatic  needle,  or  to  wind 
the  wire  so  many  times  round  the  needle ;  we  are,  consequently, 
enabled  to  construct  instruments  in  which  the  angle  of  deviation 
stands  in  a  simple  relation  to  the  force  of  the  current.  The  most 
simple  and  useful  apparatus  for  measuring  powerful  currents  is 
the  so-called  tangent  compass,  represented  at  Fig.  425.  The 
current  is  conducted  by  a  circularly  formed  vertical  copper  strip 
round  the  needle,  which  is  in  the  middle  of  the  circle,  compared 
with  whose  diameter ;  it  is  very  small.  The  current  is  conducted 
through  a  hollow  copper  cylinder,  from  which  it  passes  into  the 
circular  band,  while  the  other  end  of  the  copper  ring  is  in  con- 
nection with  a  copper  rod  passing  through  the  centre  of  the 
copper  tube,  without  being  in  contact  with  it.  Thus  the  cur- 
rent may  rise  through  the  hollow  copper  cylinder,  and  pass  over 
to  the  copper  ring,  traversing 


its  whole  length,  and  returning 
again  through  the  copper  rod, 
which  is  insulated  in  the  mid- 
dle of  the  cylinder. 

The  apparatus  is  so  placed, 
that  the  copper  ring  lies  in  the 
plane  of  the  magnetic  meridian, 
the  needle  naturally  being,  in 
this  case,  in  the  vertical  plane 
of  the  ring,  and  pointing  to  the 
0  of  the  graduated  division ; 
as  soon,  however,  as  a  galvanic 
current  passes  through  the  cop- 
per ring,  the  needle  is  made  to 
deviate,  and  the  force  of  the 


Fig.  425. 


444  FORCE    OF    THE    GALVANIC    CIRCUIT. 

current  will  be  proportional  to  the  trigonometrical  tangent  of  the 
angle  of  deviation  ;  hence  the  name  of  the  instrument. 

Force  of  the  Galvanic  Circuit. — The  agent  which  produces  the 
phenomena  of  galvanism  is  nothing  more  than  the  electricity  gene- 
rated in  the  electrifying  machine,  and  in  the  electrophorus,  only 
here  the  electricity  is  in  motion,  and  there  it  is  at  rest ;  the  one 
presents  us  with  phenomena  of  motion,  the  other  those  of  pressure ; 
the  one  affording  us  an  abundant,  the  other  a  comparatively  poor 
supply  of  electricity. 

We  may,  perhaps,  make  the  true  relation  of  the  matter  clearer  by 
an  illustration.  Thus,  we  may  compare  the  electrifying  machine 
to  a  well,  which  yields  water  but  sparingly,  but  lies  high  on  a  hill. 
The  water  may  be  collected  in  a  narrow  conducting  pipe  continued 
into  the  valley,  and  closed  below.  The  walls  of  this  tube  have 
naturally  to  sustain  a  great  pressure,  especially  at  the  lower  end, 
although  the  mass  of  water  in  the  tube  may  be  small.  At  the 
lower  end  of  the  tube  there  is  an  opening  closed  by  a  valve, 
which  is  pressed  against  the  aperture  by  a  spring  or  a  weight. 
The  more,  however,  the  column  of  water  rises  in  the  tube,  the 
stronger  will  be  the  pressure ;  and  when  the  external  counter  pres- 
sure no  longer  suffices  to  afford  resistance,  the  valve  will  be  opened, 
and  the  water  will  rush  violently  forth ;  at  the  same  time,  however, 
the  level  of  the  water  in  the  tube  will  rapidly  sink;  the  external 
pressure  will  again  acquire  a  preponderating  force,  and  close  the 
aperture.  By  degrees  the  tube  will  be  refilled,  and,  after  a  time, 
the  water  will  rise  so  high,  that  the  valve  will  be  again  opened. 

In  the  electrifying  machine,  the  conductor  is  the  vessel,  or 
conducting  pipe,  in  which  the  electricity  is  accumulated.  If  we 
bring  a  conductor,  as  the  knuckle  of  the  finger,  to  the  one  end  of 
the  conductor,  the  greatest  accumulation  of  electricity  will  take 
place ;  the  electricity  will  have  a  tendency  to  pass  to  the  finger ;  but 
the  layer  of  air  between  the  conductor  and  the  hand,  representing 
the  weight  which  holds  the  valve  down,  will  hinder  its  passage. 
It  is  only  when  the  electricity  on  the  conductor  has  accumulated 
to  a  certain  amount,  that  the  resistance  is  overcome,  the  layer  of 
air  broken  through,  and  the  conductor  partly  discharged.  On 
bringing  the  finger  still  nearer  to  the  conductor,  the  resistance 
opposed  to  the  passage  of  the  electricity  is  diminished,  which 
again  corresponds  to  the  abatement  of  the  pressure  that  keeps  the 
valve  of  the  conducting  pipe  closed. 


FORCE   OF   THE   GALVANIC   CIRCUIT.  445 

If  the  opening  at  the  lower  end  of  the  conducting  tube  were 
not  shut  by  the  valve,  the  water  would  flow  out  in  the  same  pro- 
portion as  that  supplied  by  the  spring,  and  the  accumulation  of 
the  water,  together  with  the  pressure  sustained  by  the  walls,  would 
cease.  As,  however,  the  spring  yields  only  a  small  quantity  of 
water,  very  little  will  flow  from  the  aperture,  and  the  water  which 
was  able  to  bear  so  great  a  pressure  when  accumulated  in  the 
tube,  can  scarcely  produce  any  perceptible  mechanical  effect, 
when  it  is  suffered  to  flow  freely  out. 

The  case  of  the  conductor  of  the  machine  being  brought  in 
conducting  communication  with  the  earth  or  the  rubber,  corre- 
sponds to  the  free  discharge  of  water  from  a  scantily  supplied 
spring.  All  tension,  or  accumulation  of  electricity  on  the  con- 
ductor ceases;  the  thinnest  wire  being  then  able  to  draw  off  all 
the  electricity  from  the  conductor;  while  the  freely  discharging 
electricity  scarcely  gives  the  slightest  evidence  of  those  powerful 
actions  observed  in  galvanic  apparatus. 

A  galvanic  apparatus  is  like  a  very  copious  spring  having  an 
inconsiderable  fall,  and  whose  water  is  freely  discharged  in  wide 
channels.  The  whole  mass  of  the  water  exercises  but  a  trifling 
pressure  on  the  walls ;  but  it  is  capable  of  producing  mechanical 
effects,  moving  wheels,  &c. 

If  a  large  Leyden  jar  be  discharged  by  a  thin  wire,  the  latter 
will,  as  we  have  already  seen,  become  red  hot,  owing  to  the  quan- 
tity of  electricity  passed  through  it.  The  action,  however,  is 
only  momentary,  as  all  the  electricity  accumulated  in  the  jar  by 
the  continued  turning  of  the  machine  passes  in  a  moment  through 
the  thin  wire.  The  case  is  totally  different  when  we  unite  by  a 
thin  short  wire  both  poles  of  a  galvanic  apparatus  with  large 
plates.  The  wire  will  become  red  hot  even  when  it  is  far  thicker 
than  the  wire  heated  by  the  discharge  of  the  Leyden  jar:  but 
here  the  heating  is  not  momentary,  but  continues  as  long  as  the 
current  passes  through  the  wire  ;  at  every  moment,  therefore,  the 
galvanic  apparatus  yields  incomparably  more  electricity  than  can 
be  accumulated  in  the  Leyden  jar,  by  a  continued  turning  of  the 
machine. 

Let  us  now  proceed  to  examine  the  circumstances  on  which 
depends  the  quantity  of  electricity  which  can  be  engendered  by  a 
galvanic  apparatus. 

When  two  metals  are  brought  into  contact,  if  only  at  a  few 
38 


446  FORCE    OF    THE    GALVANIC    CIRCUIT. 

points,  we  at  once  obtain  an  abundant  supply  of  electricity.  We 
have  already  seen  that  we  cannot  form  a  galvanic  apparatus  with- 
out such  bodies  as  belong  to  the  series  of  tension.  Galvanic  cir- 
cuits are  constructed  of  metals  and  fluids ;  the  latter,  however, 
are  not  good  conductors  of  electricity,  and  rank  in  this  respect 
far  below  metals.  The  moist  layers  intervening  between  the 
metal  plates  of  the  voltaic  pile  are  not  able  in  a  given  time  to 
give  a  passage  to  all  the  electricity  which  in  the  same  period  of 
time  may  possibly  be  engendered  by  the  electromotor  force  of  the 
pile.  It  will,  of  course,  be  understood  that  the  quantity  of  the 
electricity  which  can  circulate  in  such  an  apparatus,  depends 
upon  the  diagonal  section  of  the  moist  layers ;  now  as  the  diago- 
nal section  of  the  moist  conductor  in  the  voltaic  pile  depends 
upon  the  size  of  the  double  plates,  we  may,  by  increasing  the 
size  of  the  latter,  augment  the  quantity  of  the  electricity.  We 
shall  subsequently  learn  by  experimental  proofs  to  test  the  cor- 
rectness of  this  view. 

With  the  increase  of  the  plates  in  the  voltaic  pile,  the  surfaces 
of  contact  between  the  copper  and  zinc  also  increase ;  that  the 
increased  quantity  of  the  electric  current  is  not  occasioned  by 
this  circumstance  is,  however,  proved  by  the  fact  that  the  appa- 
ratus delineated  in  Figs.  401,  402,  and  404,  which  have  a  large 
diagonal  fluid  surface  intervening  between  the  copper  and  zinc, 
yield  a  considerable  quantity  of  electricity,  although  the  two 
metals  are  only  brought  into  contact  at  a  proportionally  small  sur- 
face, namely,  where  the  copper  wire  is  soldered  to  the  zinc  cylin- 
der or  plate. 

Everything,  therefore,  which  promotes  the  passage  of  electri- 
city through  the  fluid  conductor  effects  an  immediate  increase  of 
the  quantity  engendered.  The  shorter  the  course  is,  which  the 
electricity  must  traverse  in  passing  through  the  fluid,  and,  conse- 
quently, the  thinner  the  fluid  layer  between  the  metal  plates,  the 
greater  will  be  the  quantity  of  electricity  that  can  circulate  in  the 
apparatus.  Thus,  the  greater  the  conducting  power  of  the  fluid, 
and  the  closer  the  metal  plates  approximate  to  each  other  in  the 
fluid,  the  greater  will  be  the  electric  quantity  of  the  current. 

Let  us  now  inquire  into  the  influence  exercised  by  the  number 
of  the  double  plates  upon  the  galvanic  current.  If  we  suppose  a 
moist  disc  or  layer  to  be  placed  between  a  zinc  and  a  copper 
plate,  and  the  metals  united  by  a  copper  wire,  we  shall  have  a 


OHM'S    LAW.  447 

closed  simple  galvanic  circuit.  The  resistance  to  be  opposed  by 
the  current  in  the  moist  conductor  is  incomparably  greater  than 
the  resistance  opposed  by  the  wire  to  the  circulation  of  the  cur- 
rent ;  the  apparatus  yielding  far  more  electricity  than  the  moist 
conductor  can  transmit.  If  we  double  the  number  of  elements, 
connecting  the  uppermost  copperplate  by  a  copper  wire  with  the 
lowest  zinc  plate,  we  shall  have  a  circuit  of  two  elements.  The 
question  here  arises,  as  to  whether,  by  this  arrangement,  a  larger 
quantity  of  electricity  can  be  made  to  circulate  than  in  the  above 
considered  simple  circuit? 

In  the  simple  circuit,  the  quantity  of  the  circulating  electricity 
is  limited  by  the  resistance  of  the  moist  conductor;  now,  this 
resistance  is  doubled  by  the  second  moist  layer;  but  then,  on  the 
other  hand,  the  tension  urging  the  passage  of  the  electric  current 
has  become  twice  as  great,  and,  consequently,  an  equal  quantity 
of  electricity  will  circulate  in  both  cases.  The  increase  of  the  num- 
ber of  double  plates  does  not  tend  to  augment  the  quantity  of  the 
circulating  electricity  when  the  circuit  is  perfectly  closed,  since, 
in  this  case,  it  is  quite  immaterial  whether  we  use  one  or  many 
pairs  of  plates.  In  an  imperfectly  closed  circuit,  however,  that 

j  is,  where  a  bad  conductor  has  been  made  to  complete  the  circuit, 
many  plates  must  be  made  use  of,  as  a  greater  degree  of  electric 
tension  is  necessary  to  force  a  passage,  as  it  were,  through  the 

i  bad  conductor.  The  intensity  of  the  galvanic  current  is  propor- 
tional to  the  number  of  the  double  plates. 

Ohm's  Law. — The  above  indicated  relations  of  the  force  of  the 
current  with  reference  to  the  elements  of  the  circuit  have  been 
reduced  by  Ohm  to  strict  mathematical  formula.  By  means  of 

i  the  law  named  after  him,  (of  which  we  shall  treat  presently),  a 
secure  basis  was  first  given  to  the  investigations  made  on  the  force 
3f  the  electric  current. 

In  order  that  an  electric  current  may  pass  through  a  conductor, 
[t  is  indubitably  necessary  that  the  electricity  should  have  an  un- 
equal degree  of  tension  at  different  parts  of  the  conductor.  If, 

(i  jbr  instance,  we  touch  the  conductor  of  an  electrifying  machine 
Ivith  a  wire,  the  electricity  will  be  propelled  through  the  latter, 
olely  on  account  of  the  strong  tension  of  the  electricity,  which 
.rives  it  through  the  wire  to  the  conductor,  there  being  a  greater 
ccumulation  of  electricity  at  the  end  of  the  wire  in  contact  with 
ie  conductor  than  at  the  opposite  end ;  thus,  on  connecting  to- 


I 


448  OHM'S    LAW. 

gether  by  means  of  a  wire,  two  similar  conductors  equally  stronglj 
charged  with  electricity,  no  current  will  be  formed. 

When  the  Voltaic  pile  is  insulated,  the  opposite  electricities  al 
the  poles  will  be  in  a  state  of  tension,  and  this  condition  cannot, 
possibly,  entirely  cease,  on  connecting  the  two  poles  by  a  conduc- 
tor, since  no  +  electricity  can  flow  from  the  +  pole  if  there  be  noi 
here  a  greater  accumulation  of  the  same  kind  of  electricity;  £ 
certain  tension,  like  a  certain  pressure,  as  it  were,  is  necessary 
to  occasion  a  motion,  by  which  the  resistances  may  be  overcome 
in  the  conductor  through  which  the  current  is  to  pass. 

The  quantity  of  electricity  passing  through  a  conductor  depend: 
essentially  upon  two  circumstances;  first,  on  the  resistance  to  be 
overcome  in  the  conductor;  and  next,  on  the  tension  or  pressure 
urging  the  electricity  through  the  conductor  ;  it  will  now  be  easily 
seen,  that  the  quantity  of  electricity  passing  in  a  given  time 
through  some  specified  conductor,  must  stand  in  an  inverse  rela- 
tion to  the  resistance  in  the  conductor,  and  in  a  direct  relation  t( 
the  electric  tension  urging  the  current  through  the  conductor 
The  tension  is  here  to  a  certain  extent  the  accelerating  force. 

The  quantity  of  electricity  passing  through  a  conductor,  tha 

V 

is,  the  force  of  the  current,  may  be  expressed  by  —,ifE  desig- 

JL 

nate  the  electric  tension  engendered  by  the  current,  and  L  the 
resistance  to  be  overcome  in  the  conductor. 

Let  us  here  consider  the  current  of  one  simple  closed  voltaic 
element.  Let  e  be  the  tension  occasioned  by  the  current,  a,  the 
resistance  in  the  circuit  itself,  and  /  that  in  the  wire  closing  the 

/> 

circuit;  then  the  force  of  the  current^  = 


If  we  had  combined  n  such  elements  into  a  column,  the 
electric  tension,  setting  in  motion  the  current,  would  be  n  e  ;  bu 
the  resistance  in  the  circuit  being  increased  in  an  equal  proper 
tion,  as  it  has  to  be  overcome  not  only  in  one  element,  but  in  j 
elements,  the  resistance  in  the  conductor  will  be  now  n  a,.  li 
now,  the  arc,  closing  the  circle,  is  the  same  as  in  the  simple  cir 

77    P 

cuit,  we  have  for  the  force  of  the  current  pl  =  -  -,. 

7171  -f   / 

If  I  were  very  small,  in  comparison  with  x,  the  above  give: 

P  71   ( 

value  of  p  would  be  nearly  -,  but  the  value  of  p1  would  be  — 


OHM'S    LAW.  449 

consequently,  also,  =  ?;  if,  therefore,  the  resistance  in  the  arc, 

closing  the  circuit,  be  small  in  comparison  with  the  resistance  of 
one  single  element,  the  increase  of  the  elements  will  afford  no 
advantage.  On  the  other  hand,  an  increase  of  the  elements  will 
occasion  an  increase  in  the  force  of  the  current,  if  /  be  very  large ; 
that  is,  if  there  be  a  considerable  resistance  to  be  overcome  in  the 
arc  closing  the  circuit. 

We  will  now  consider  the  influence  exercised  on  a  simple  cir- 
cuit, by  an  increase  of  its  surface.     The  force  of  the  current,  for 

a  single  element,  was  designated  above  as  p  =  -  '- — ;  if,  now, 

^  -p  If 

the  surface  of  the  voltaic  elements  be  increased  n  times,  without 
altering  anything  else,  the  only  result  will  be  to  make  the  resist- 
ance in  the  circuit  itself  n  times  smaller,  owing  to  the  diagonal 
section  of  the  fluid,  through  which  the  current  must  pass,  becom- 
ing n  times  greater;  instead,  therefore,  of  the  resistance  si,  we 

shall  now  have  -,  and,  consequently,  the  force  of  the  current  pn 
ill  now  be, 


>r,  what  is  the  same  thing, 


If  I,  that  is  to  say,  the  resistance  in  the  arc  closing  the  circuit, 
rere  null,  the  force  of  the  current  would  be  proportional  to  the 
iperficies  of  the  electric  element ;  and  this  is  very  nearly  the 
ise  when  I  is  extremely  small;  an  increase  of  surface  produces, 
lerefore,  an  increase  in  the  force  of  the  current,  if  the  resistance 

the  closing  arc  be  small  in  proportion  to  the  resistance  in  the 
Ircuit  itself. 

The  values  for  the  resistances  in  the  circuit  itself,  and  in  the 

sing  arc,  must,  as  we  shall  presently  see,  be  referred  to  the 
|me  unit. 

I  These  laws  are  fully  confirmed  by  experiment. 
I  In  order  to  show  that  the  force  of  the  current  stands  in  an 

rerse  relation  to  the  length  of  the  closing  arc,  we  have  merely 
I  complete  the  circuit  of  a  galvanic  element  (for  instance,  one  of 

38* 


450 


OHM'S   LAW. 


BecquerePs  elements)  by  a  tangential  compass,  and  then  insert, 
according  to  the  series,  pieces  of  wire  of  different  length,  noting 
each  time  the  corresponding  deviation. 

A  series  of  experiments  of  this  kind  gave  the  following  results : 


Length  of  the  copper  wires 
inserted. 

Deviation  observed. 

Tangents  of  the  angles 
of  deviation. 

0  metre. 

62°  00' 

1,880 

5     "         16  ft.  4  in. 

40    20 

0,849 

10     "        32  "  9  " 

28    30 

0,543 

40     "        45  "  0  " 

9    45 

0,172 

70     "        77  "  3  " 

6     00 

0,105 

100     "       110  "  1  " 

4     15 

0,074 

We  observe,  here,  no  regularity  in  the  decrease  of  the  intensity 
of  the  current  on  lengthening  the  inserted  wire ;  but,  when  we 
consider  that  this  wire  is  not  the  only  resistance  to  the  current, 
and  that  in  the  electromotor  apparatus  itself,  and  in  the  different 
parts  of  the  compass  through  which  the  current  passes,  a  resist- 
ance has  to  be  overcome,  which  we  will  designate  as  the  resistance 
of  the  element,  it  will  be  evident  that  this  last  named  resistance 
may  be  estimated  as  equal  to  the  resistance  of  a  copper  wire  of 
the  same  thickness  as  the  one  inserted,  and  of  the  unknown  length 
x ;  the  following,  therefore,  are  actually  the  corresponding  lengths 
of  the  circuit,  and  of  the  angles  of  deviation. 


Length  of  the  chain. 

Deviation  observed. 

Tangents  of  the 
angle  of  deviation. 

X 

62°  00' 

1,880 

x  +      5,    16  ft.  4  in. 

40  20 

0,849 

x  +    10,    32  "  9  " 

28   30 

0,543 

x  +    40,    45  "  0  " 

9  45 

0,172 

x  +    70,    77  «  3  " 

6   00 

0,105 

x  +  100,  110  «  1  « 

4   15 

0,074 

If,  now,  the  force  of  the  hydro-electric  currents  is  actually  in- 
versely as  the  length  of  the  circuit,  the  numbers  of  the  first  column 
must  be  inversely  as  the  numbers  of  the  last,  and,  consequently, 
x  :  x  +  5  =  0,849  :  1,880,  whence  it  follows  that  x  =  4,11.  If, 
in  the  same  manner,  we  compare  the  first  observation  with  all 


OHM'S    LAW. 


451 


those  succeeding  it,  we  shall  always  obtain  the  same  value  fora:; 
and,  indeed,  the  values  thus  computed  for  x  are  very  nearly  equal 
to  each  other :  we  find,  for  instance,  besides  the  value  already 
computed,  4,06  (13,28  ft.),  4,03  (13,15  ft),  4,14  (13,58  ft.),  and 
4,09  (13,45  ft.),  metres.  The  mean  of  which  is  4,08  (13,36  ft.). 
The  resistance  of  the  element  is,  therefore,  equal  to  the  resist- 
ance of  a  copper  wire,  4,08  metres  (13,36  ft.)  in  length,  and  of 
the  same  thickness  as  the  one  inserted.  If  we  make  this  length 
our  standard,  we  may  easily,  by  aid  of  the  general  law,  that  the 
force  of  the  current  is  inversely  as  the  length  of  the  circuit, 
compute  the  deviations  that  will  be  obtained,  and  then  compare 
them  with  those  directly  observed,  as  has  been  done  in  the  follow- 
ing table. 


The  com- 

The deviation 

Length  of  the 

circuit. 

puted  devia- 

actually ob- 

Difference. 

tion. 

served. 

4,08  metres, 

13,36  ft. 

62°  00' 

62°  00' 

9,08       " 

29,79  " 

40   18 

40   20 

+    2 

14,08      " 

46,19  " 

28  41 

28   30 

—  11 

44,08       " 

144,62  « 

9   56 

9   45 

—  11 

74,08       " 

243,05  " 

5   57 

6   00 

-f    3 

104,08       " 

341,47  « 

4   14 

4   15 

+    1 

Such  an  accordance  between  the  results  of  observation,  and 
those  derived  from  a  general  law,  leaves  no  doubt  as  to  the  cor- 
rectness of  that  law. 

In  order  to  show  that,  in  a  perfectly  closed  circuit,  that  is,  where 
the  resistance  in  the  conductor  is  very  inconsiderable,  the  number 
of  the  elements  does  not  increase  the  force  of  the  current  in  the 
closing  arc,  we  must  successively  complete  a  circuit,  composed 
of  1,  2,  3,  or  4  elements,  through  the  tangential  compass,  and 
then  observe  the  corresponding  deviation.  A  series  of  experiments 
of  this  kind,  gave  the  following  results : 

Number  of  elements.  Deviation  observed. 

1  69° 


66,5 

67,5 

67 

68 

64 


452  THE    CONDUCTIBILITY    OF    METALS. 

We  see  here,  that  the  force  of  the  current  remains  almost  en- 
tirely unchanged,  not  increasing  with  the  addition  of  the  elements. 
The  reason  of  its  not  remaining  wholly  unchanged  is,  that  the  in- 
dividual elements  are  not  perfectly  equal. 

Where,  however,  there  is  a  considerable  resistance  to  be  over- 
come, the  force  of  the  current  is  certainly  increased  with  the 
number  of  the  elements.  Six  elements,  closed  by  the  tangential 
compass,  yielded  a  deviation  of  39°  after  the  insertion  of  a  wire 
40  yards  in  length. 

One  element,  closed  in  the  tangential  compass  by  the  same  wire, 
measuring  40  feet  in  length,  only  showed  a  deviation  of  11°. 

Capacity  of  Metals  for  conducting  Electric  Currents,  or  the 
Conductibility  of  Metals. — In  the  experiments  given,  (at  p.  450,) 
pieces  of  wire,  varying  in  length,  were  inserted  in  the  closing 
arc  of  the  circuit,  and  the  relation  of  the  force  of  the  current  to 
the  length  of  the  closing  wire  was  thus  obtained.  If,  now,  we 
insert  into  the  closing  arc,  wires  of  equal  length,  but  of  unequal 
thickness,  composed  of  the  same  metal,  and  still  observe  the 
corresponding  deviations  of  the  needle  of  the  tangential  compass, 
we  shall  ascertain  from  these  experiments  the  relation  that  the 
force  of  the  current  bears  to  the  thickness  of  the  wires  ;  and  here 
we  find,  that  the  force  of  the  current  is  proportional  to  the  trans- 
verse section  of  the  wires;  or,  in  other  words,  that  two  wires,  com- 
posed of  the  same  metal,  will  exercise  an  equal  resistance,  if  their 
lengths  are  inversely  as  their  transverse  sections. 

In  order  to  compare  the  conductibility  of  different  metals,  no 
method  is  simpler,  or  more  certain,  than  to  conduct  the  current  of 
a  sufficiently  powerful  element  through  a  tangential  compass,  to 
insert  wires  of  different  metals  in  the  closing  arc,  and  to  observe 
the  corresponding  deviations. 

The  following  are  the  numbers  expressing  the  capacity  of  dif- 
ferent metals  for  conducting  electric  currents : 

Silver  .         .         .         .136 

Gold  ....     103 

Copper  .        .        .         .100 

Zinc  ....       28 
Platinum  ...       22 

Iron  ....       17 

Mercury  ....         2,6. 


THE   CONDUCTIBILITY   OF   METALS.  453 

That  is  to  say,  a  copper  wire  of  100  feet  in  length,  offers  as 
great  a  resistance  to  an  electric  current,  as  equally  thick  wires  of 
silver,  zinc,  platinum,  iron,  &c.,  which  are  respectively  136,  28, 
22,  or  17  feet  in  length. 

The  conducting  power  of  fluids  is  very  small  in  comparison  to 
that  of  metals:  thus,  ex.  gr.,  the  conducting  power  of  platinum 
is  2J  million  times  as  great  as  that  of  a  solution  of  sulphate  of 
copper ;  while  the  conducting  power  of  distilled  water  is  only 
0,0025  of  the  conducting  power  of  a  solution  of  sulphate  of 
copper. 


454 


MAGNETIC    ACTIONS    OF    THE    CURRENTS. 


PART  IV. 

ELECTRO -MAGNETISM. 


CHAPTER  I. 


MAGNETIC  ACTIONS  OF  THE  CURRENT. 

WE  have  already  remarked  that  the  electric  current  is  capable 
of  making  the  magnetic  needle  deviate,  and  it  now  remains  for  us, 
without  entering  further  into  these  magnetic  actions,  to  pass  to  the 
consideration  of  the  applications  that  have  been  made  of  the  devia- 
tion of  the  magnetic  needle,  to  ascertain  the  laws  of  the  force  of 
the  current.  The  following  chapter  is  devoted  to  the  further  con- 
sideration of  the  magnetic  actions  of  the  electric  current. 

Magnetization  by  the  Galvanic  Current. — The  electric  current 
acts  not  only  on  free  magnetism,  but  is  likewise  capable  of  sepa- 
rating the  still  combined  magnetic  fluids.  In  order  to  show  the 
action  of  the  current  on  soft  iron,  we  need  only  plunge  the  wire 
into  iron  filings,  or  strew  them  over  it  during  the  passage  of  the 
Fig  426  Fig  427  galyanic  current.  The  iron  filings  remain  hang- 
U  £  ing  to  the  wire  until  the  current  is  broken ;  small 

steel  needles  may  be  converted  into  permanent 
magnets  by  means  of  the  galvanic  current;  in 
order,  however,  to  render  the  current  very  active, 
we  must  make  it  pass  transversely  round  the 
needle,  as  is  the  case  in  the  arrangement  we  are 
about  to  describe.  A  copper  wire  is  wound  spi- 
rally round  a  glass  tube,  in  which  a  steel  needle 
is  placed  (see  Fig.  426).  If  now  we  let  a  current 
pass  through  the  convolutions  of  the  wire,  the 
needle  will  become  permanently  magnetic,  and  it 
is  only  necessary  that  the  current  should  pass 
through  it  for  the  space  of  a  minute,  to  magnetize 
the  needle  as  perfectly  as  possible. 


MAGNETIZATION   BY   THE   GALVANIC   CURRENTS.        455 

We  distinguish  right-handed  helices  as  seen  in  Fig.  426,  from 
left-handed  helices  as  seen  in  Fig.  427.  In  the  former,  the  con- 
volutions run  in  the  same  manner  as  in  a  cork-screw,  or  in  an 
ordinary  screw. 

In  right-handed  helices  the  north  pole  (that  is  the  south  end) 
is  at  that  end  of  the  needle  where  the  -f  current  enters  it,  while, 
in  the  left-handed  helix,  the  north  pole  is  at  the  extremity  from 
whence  the  current  passes  out.  In  the  figures,  the  north  pole  is 
designated  as  6,  and  the  south  pole  as  a. 

We  may  make  magnets  of  soft  iron  by  means  of  the  galvanic 
current,  far  surpassing  all  steel  magnets  in  force.  For  this  pur- 
pose, it  is  only  necessary  to  encircle  a  strong  horse-shoe  of  soft 
iron  with  thick  copper  wire,  in  the  way  represented  in  Fig.  428. 
The  copper  wire  must  be  covered  with  silk,  in  order  that  the  cur- 
rent may  not  pass  laterally  from  one  winding  to  another,  (these 
windings  lying  close  together,)  or  be  trans- 
ferred to  the  iron,  but  traverse  the  wire  in 
its  whole  length.  The  wire  is  twisted 
round  the  curved  lines  of  a  horse-shoe, 
passing  round  in  the  same  direction,  but 
somewhat  inclined  to  the  right;  if,  there- 
fore, the  -f  current  enters  at  c,  a  north 
pole  will  be  formed  there,  and  a  south  pole 
at  b.  By  means  of  a  holder,  we  may  sus- 
pend weights  to  a  magnet  of  this  kind. 
Thus,  a  magnet  whose  diameter  is  about  2  or  3  inches,  and  whose 
limbs  are  about  1  foot  or  1,5  feet  in  length  may  sustain  a  weight 
of  from  800  to  lOOOlbs.,  provided  the  wire  be  thick,  and  the  cur- 
rent passing  through  it  be  of  sufficient  strength.  As  electro-mo- 
tors for  these  electro-magnets,  simple  circuits  of  a  large  area  are 
used,  or  Groves''  or  Bunsens^  elements;  for  this  purpose,  however, 
all  the  zinc  cylinders  must  be  connected  together,  in  the  same 
manner  as  all  the  carbon  cylinders  or  platinum  plates.  The  mag- 
netism vanishes  as  the  current  ceases. 

As  we  can  engender  a  temporarily  powerful  magnetism  in  soft 
iron  by  the  galvanic  current,  we  are  also  able  to  produce  steel 
magnets  of  great  force  by  the  same  means.  An  arrangement 
especially  applicable  to  this  purpose  is  the  wire  coil  constructed  by 
Elias,  and  represented  in  Fig.  429. 

A  copper  wire  about  25  feet  in  length,  and  Jth  of  an  inch  in 


456  GALVANIC    CURRENT    AS    A   MOVING   FORCE. 

thickness,  must  be  properly  encircled  with  silk,  and  then  wound 
into  a  coil,  as  seen  in  the  figure.  The  height  of  the  wire  coil 
amounts  to  about  1  inch,  and  the  diameter  of  the  inner  cavity  to 
1J  inches.  The  two  extremities  of  the  wires  are  brought  into 
connection  with  the  poles  of  a  powerful  voltaic  element  when  we 
want  to  magnetize  a  steel  rod. 

Fig.  429. 


Whilst  a  strong  current  circulates  through  the  wire  coils,  the 
steel  staff  or  rod  must  be  inserted  into  the  coil,  and  moved  back- 
ward and  forward,  and  when  the  middle  part  is  a  second  time  in 
the  coil,  the  circuit  is  opened,  and  the  rod  can  then  be  taken  out 
perfectly  magnetized. 

It  is  best  to  put  a  piece  of  soft  iron  above  and  below  the  steel 
rod,  and,  if  the  rod  to  be  magnetized  be  of  a  horse-shoe  shape, 
it  should  be  provided  with  a  holder  during  the  operation. 

Application  of  the  Galvanic  Current  as  a  Moving  Force. — The 
powerful  magnetic  actions  which  the  electric  current  is  capable  of 
producing,  have  led  to  the  idea  of  applying  them  as  a  moving 
power.  Fig.  430  shows  an  apparatus  which  is  well  adapted  to 
exhibit  the  manner  in  which  a  continuous  motion  may  be  pro- 
duced by  the  magnetizing  action  of  the  galvanic  current. 

Ji  B  is  a  piece  of  soft  iron  curved  into  the  form  of  a  horse-shoe, 
and  fixed  to  a  stand,  being  encircled  by  a  copper  wire  in  the  man- 
ner indicated  in  the  electro-magnet  in  Fig.  428.  The  one  end 
of  the  wire  goes  to  the  brass  column  a,  the  other  to  6,  the  poles 
of  a  .powerful  galvanic  element  are  attached  at  a  and  6,  and  the 
iron  A  B  is  thus  converted  into  a  magnet. 

Within  the  horse-shoe  JJ  B,  a  similar  smaller  one  C  D,  is  in- 
troduced, which  rotates  about  a  vertical  axis.  This  iron  C  D  is 
likewise  encircled  by  a  copper  wire  in  the  manner  indicated,  the 
two  ends  of  the  wire  being  plunged  into  a  wooden  ring-shaped 
channel  filled  with  mercury.  This  channel  is  divided  into  two 


GALVANIC    CURRENT   AS   A   MOVING   FORCE. 


457 


parts  by  means  of  a  wooden  or  ivory  partition,  the  one  part  being 
in  communication  by  means  of  a  copper  wire  with  the  brass 
column  c,  and  the  other  with  the  brass  column  d.  (The  two 
poles  of  a  simple  circuit  are  attached  at  c  and  d.  (The  two 
partitions  must  now  be  filled  with  mercury  to  such  a  height  that 
the  level  may  project  beyond  the  partition  walls,  although  not  so 

Fig.  430. 


as  to  pass  from  one  space  to  the  other,  which  may  easily  happen, 
owing  to  the  mercury  forming  a  convex  drop,  as  it  were,  in  each 
division.  The  two  ends  of  the  electro-magnet  C  D  penetrate 
sufficiently  far  into  the  vessel  so  as  to  dip  into  the  mercury  on 
either  side  of  the  partition  wall,  but  in  such  a  manner  as  to  admit 
of  their  passing  freely  over  it  during  the  rotation  of  the  electro- 
magnet C  D.  In  the  position  of  the  electro-magnet  C  D  repre- 
sented in  Fig.  430,  supposing  the  +  pole  of  a  powerful  galvanic 
element  to  be  connected  at  c,  and  its  —  pole  at  d,  the  +  current 
will  pass  from  c  to  the  left  division  of  the  channel,  from  whence 
it  will  go  through  the  copper  wire  round  the  moving  horse-shoe 
from  D  to  C,  then  from  C  into  the  right  division  of  the  channel, 
39 


458  GALVANIC    CURRENT    AS    A   MOVING    FORCE. 

and  from  thence  to  d.  In  this  position,  the  pole  C  will  be  at- 
tracted by  Ay  and  D  by  B,  by  which  a  rotatory  motion  of  the 
electro-magnet  C  D  will  be  induced.  But  now  when  C  reaches 
A^  and  D  reaches  B,  the  two  ends  of  the  wire  of  the  inner  elec- 
tro-magnet will  pass  over  the  partition  wall :  the  current  that 
makes  C  D  magnetic,  will  be  interrupted  for  a  moment ;  as  soon, 
however,  as  the  ends  of  the  wires  have  passed  from  one  division 
into  the  other,  the  current  will  go  in  an  opposite  direction  through 
the  copper  wire  encircling  C  D,  the  pole  C  will  then  be  repelled 
by  A,  and  D  by  B,  whilst  C  and  B  and  D  and  A  will  attract  each 
other,  thus  the  rotation  of  the  inner  electro-magnet  will  be  con- 
tinued until  C  comes  to  B,  and  D  to  A,  and  by  another  inversion 
of  the  poles  of  the  inner  electro-magnet,  the  rotation  of  the  latter 
will  be  continued  in  an  opposite  direction. 

A  notched  wheel  is  secured  to  the  rotatory  axis  of  the  inner 
electro-magnet,  and  connected  with  a  second  wheel  of  larger  dia- 
meter. Around  the  axis  of  the  latter  a  string  is  wound,  which 
passes  over  a  pulley,  and  supports  a  hanging  weight  that  is  lifted 
by  the  rotation  of  the  inner  electro-magnet. 

This  apparatus  is  merely  an  improvement  upon  Ritchie's  rota- 
tion apparatus,  in  which  a  steel  magnet  supplies  the  place  of  the 
external  electro-magnet,  whilst  the  rotating  iron  has  the  form  of 
a  straight  rod  surrounded  by  a  wire,  the  extremities  of  which  are 
immersed  in  a  channel  filled  with  mercury,  as  in  our  apparatus, 
the  rotation  being  maintained  by  the  inversion  of  the  poles  suc- 
ceeding every  semi-revolution. 

The  attempts  made  by  Jacobi  in  Petersburg,  and  Wagner  in 
Frankfort,  to  apply  the  galvanic  current  practically  as  a  moving 
power,  have  not  hitherto  afforded  the  desired  results. 

Another  practical  application  of  the  magnetization  of  soft  iron, 
by  galvanic  currents,  has  been  made  use  of  in  the  Electric  Tele- 
graph, the  arrangement  of  which  is  essentially  as  follows.  If  the 
two  extremities  of  a  wire,  encircling  a  U-shaped  piece  of  soft  iron, 
be  made  so  long  as  to  pass  many  miles,  to  some  distant  place,  at 
which  there  is  a  galvanic  circuit,  we  may,  by  alternately  closing 
and  opening  this  circuit  with  the  wire  ends,  communicate  mag- 
netism to,  or  remove  it  from,  the  distant  iron ;  and,  thus,  we  may, 
consequently,  cause  the  electro-magnet  alternately  to  attract,  and 
again  to  repel  an  armature,  the  motion  of  which  is  by  means  of 
a  tooth  of  the  wheel  conveyed  to  the  hand  of  a  disc,  round  the 


GALVANIC    CURRENT    AS    A   MOVING    FORCE.  459 

margin  of  which  the  letters  of  the  alphabet  are  marked.  If  the 
hand  be  properly  placed,  it  will  move  to  Jl  on  the  first  closing  of 
the  circuit,  to  B  on  the  succeeding  opening,  and  to  C  on  a  second 
closing,  and  so  forth.  We  may,  thus,  bring  the  hand  to  any 
number  of  letters,  after  the  corresponding  number  of  openings 
and  closings  of  the  circuit,  and,  consequently,  designate  words 
and  sentences,  no  less  than  single  letters. 

[Since  the  above  was  written,  by  Professor  Miiller,  the  electro- 
magnetic telegraph  has  been  greatly  improved,  and  has  become 
of  vast  importance,  in  this  country,  as  a  mode  of  transmitting 
intelligence,  from  one  place  to  another,  with  the  utmost  speed 
and  certainty.  It  may,  therefore,  be  of  interest  to  give  a  slight 
sketch  of  the  history  of  this  invention,  before  describing  the  in- 
struments now  in  most  general  use.  This  has  been  derived  from 
various  sources,  the  principal  of  which  are,  "  The  American 
Electro-Magnetic  Telegraph,"  by  Vail;  the  "Manual  of  Mag- 
netism," by  Davis;  and  the  article,  "Telegraph,"  in  the  Ency- 
clopedia Americana,  vol.  xiii.  575. 

The  first  electric  telegraph  appears  to  have  been  devised  by 
Lesage,  at  Geneva,  in  1774.  It  consisted  of  twenty-four  pro- 
perly insulated  wires,  each  terminating,  at  one  end,  in  a  pith  ball 
electroscope;  when  the  other  end  of  any  one  of  these  wires  was 
put  in  communication  with  the  prime  conductor  of  an  electrical 
machine,  the  ball  became  repelled,  and  a  corresponding  letter  was 
indicated.  Numerous  other  telegraphs,  of  a  similar  character, 
were  proposed,  from  time  to  time,  by  Lomond,  in  1787;  by  Rei- 
zen,  in  1794;  and  by  Salva  and  Belancourt,  in  1798,  and  a  very 
ingenious  one  by  Ronalds,  in  1816.  In  all  these,  the  common 
electrical  machine  being  used,  no  important  results  were  obtained 
from  the  very  nature  of  the  instruments  employed,  and  the  tend- 
ency of  the  electricity  itself  to  be  dissipated  during  its  passage. 
In  1800,  the  discoveries  of  Volta  opened  a  new  field,  and  in  1809, 
Simmering  first  suggested  a  galvanic  telegraph,  founded  on  the 
property  of  the  current  to  decompose  water;  his  plan,  however, 
vvas  not  made  public  until  1811,  a  year  previous  to  which  Dr. 
voxe,  of  Philadelphia,  passed  signals  along  a  wire,  of  a  mile  in 
ength,  and  proposed  a  telegraph,  founded  on  the  instantaneous 
mssage  of  the  current,  and  its  property  of  producing  chemical 
hanges  upon  prepared  paper.  His  plan  was  published,  in  1816, 
n  Thompson's  Annals  of  Philosophy. 


460  GALVANIC    CURRENT   AS   A   MOVING   FORCE. 

It  was  not,  however,  until  after  the  discovery  by  Oersted,  in 
1820,  of  the  action  of  a  galvanic  current  on  a  magnet,  that  any 
truly  practical  results  were  obtained,  the  first  of  which  were 
founded  on  the  proposal  of  Ampere  to  employ  the  electro-mag- 
netic current  to  transmit  intelligence,  by  observing  the  deflection 
it  caused  in  the  needle,  instead  of  its  action  upon  water.  The 
instrument,  founded  on  this  idea,  had  the  disadvantage  of  requir- 
ing a  wire  for  each  signal,  as  well  as  one  to  return  the  current  to 
the  battery.  After  this,  numerous  other  plans  were  devised,  among 
which,  the  most  important  are  those  of  Wheatstone,  in  England, 
in  1840;  of  Schilling,  in  Russia,  in  1832;  of  Gauss  and  Weber, 
in  Gottingen,  in  1833 ;  and  by  Steinheil,  in  Munich,  about  1837. 
It  would  be  impossible  to  notice  these,  and  many  others  of  the 
kind,  and  we  must,  therefore,  refer  to  the  authorities  above  quoted 
for  their  history  and  mode  of  operation. 

The  electro-magnetic  telegraph  now  in  use  in  this  country,  is 
claimed  to  have  been  suggested,  in  1832,  by  Dr.  C.  T.  Jackson 
and  Professor  Morse,  but  was  not  patented  by  the  latter  until 
1837 ;  and  finally  matured  and  put  in  operation,  between  Balti- 
more and  Washington,  in  1844.  This  form  is  exceedingly  effi- 
cient and  simple,  and  was  the  first  devised  that  recorded  the  mes- 
sage sent  by  it ;  thus  dispensing  with  the  uncertain  attention  of 
an  assistant.  The  signals  in  this  are  not  made  by  indicating  the 
letters  of  the  alphabet,  but  arbitrary  signs,  composed  of  variously 
arranged  dots  and  lines. 

Its  operation  is  as  follows :  the  electrical  current  is  generated 
by  any  constant  battery,  (Groves'  is  usually  preferred,)  passes 
from  the  transmitting  to  the  receiving  station  by  means  of  a  con- 
necting wire,  which,  at  the  latter  place,  is  coiled,  in  the  usual 
manner,  around  the  legs  of  a  U-shaped  bar  of  soft  iron ;  this  bar 
is,  of  course,  rendered  magnetic  during  the  action  of  the  current. 
The  keeper  of  the  magnet  is  placed  upon  one  end  of  a  lever,  the 
other  end  of  which  is  armed  with  one  or  more  points,  which, 
when  the  keeper  is  suddenly  drawn  downwards,  by  the  magnetic 
action,  strike  upwards  into  a  groove,  or  grooves,  in  a  steel  roller 
situated  above  them.  Under  this  roller  passes  a  slip  of  paper, 
which,  being  unrolled,  by  machinery,  from  a  cylinder,  during  the 
action  of  the  acting  agent,  receives  a  mark  from  the  points 
attached  to  the  keeper.  The  circuit  is  completed,  or  broken,  by 
means  of  a  metallic  spring  or  key,  connected  with  one  pole  of  the 


GALVANIC    CURRENT   AS   A   MOVING   FORCE. 


461 


battery,  which  may  be  pressed  down  by  the  finger,  upon  a  metal 
stud  connected  with  the  other  pole.  When  pressed  down,  the 
circuit  is  complete ;  when  the  pressure  is  removed,  the  spring, 
rising  by  its  elasticity,  the  circuit  is  broken.  The  wires,  between 
the  stations,  are  stretched  upon  poles;  but  great  inconvenience 
has  arisen  from  their  breaking,  and  from  the  effects  of  atmospheric 
electricity ;  and  it  will,  probably,  become  necessary  to  resort  to  the 
plan  proposed  by  Mr.  Bain,  or  to  some  analogous  mode  of  insu- 
lating them  under  ground. 

Fig.  431  represents  the  recording  part  of  the  telegraph.     It 

Fig.  431. 


consists,  as  has  been  stated,  of  an  electro-magnet,  armature,  and 
.ever ;  one  end  of  which  marks  the  strip  of  paper,  by  means  of  a 
alunt  point,  when  the  instrument  is  in  action. 

Fig.  432  shows  the  telegraph  with  the  clock-work  usually  em- 
ployed.    The  electro-magnet  Jl  and  the  lever  are  the  same  as  in 

Fig.  432. 


462 


GALVANIC    CURRENT   AS   A   MOVING   FORCE. 


Fig.  433. 


the  simpler  instrument,  but  connected  with  them  is  an  apparatus 
moved  by  clock-work,  designed  to  carry  the  paper  as  it  is  un- 
wound from  a  cylinder  S,  by  the  rollers,  between  which  it  passes 
and  receives  the  registering  mark.  The  primary  movement  of 
the  lever  is  to  set  the  clock-work  in  action,  and  a  break  and  fric- 
tion wheel  are  sometimes  added,  so  as  to  stop  it  after  a  cessation 
of  the  transmission  of  signals.  A  bell  B  is  connected  with  the 

lever,,  to  apprize  the  attendant 
of  the  instant  of  the  commence- 
ment of  the  operation. 

Fig.  433  is  a  representation 
of  the  instrument  usually  em- 
ployed to  complete  or  break 
the  circuit,  by  which  the  sys- 
tem of  lines  and  dots,  repre- 
senting the  different  letters  and 
numbers,  are  produced  at  the 
other  end  of  the  telegraph. 
The  signs  employed  by  Professor  Morse,  are  as  follows : 

P--  —  2 

q 3 

r   _     --  4 

s 5 

t   6 

u 7 

v 8 

w 9 

y  --   -- 

z — 

&c.  - 


These  characters,  being  formed  by  various  combinations  of 
dots, — or  of  long  and  short  lines,  are,  of  course,  capable  of  being 
indefinitely  changed,  as  may,  from  time  to  time,  be  arranged  by 
the  conductors  of  the  telegraph.  In  sending  a  message,  a  short 
space  is  used  between  each  letter  of  a  word,  longer  ones  between 
the  words,  and  still  longer  between  sentences. 


INFLUENCE   OF   TERRESTRIAL   MAGNETISM. 


463 


Instead  of  a  galvanic  series,  a  magneto-electric  machine  may 
be  employed  for  working  the  telegraph,  and  the  whole  apparatus 
is  susceptible  of  a  variety  of  modifications  to  increase  its  efficiency 
and  certainty,  many  of  which  will  be  found  described  and  figured 
in  Davis's  Manual.  Contrivances  have,  also,  been  applied  to  it, 
which  enables  the  machine  to  print  the  message  in  the  usual  let- 
ters— of  this  character  are  modifications  of  Bain,  in  London,  and 
House,  in  this  country ;  but  they  are,  of  course,  somewhat  com- 
plicated, and  it  has  been  thought  best  to  notice  the  apparatus  in 
one  of  its  most  simple  forms.] 

Direction  of  Currents  by  the  influence  of  Terrestrial  Magnetism. 
— Since  the  current  exercises  an  influence  on  magnets,  we  cannot 
doubt  that  a  like  action  is  conversely  transferred  by  magnets  to 
the  current,  and  that  they  are  able  to  direct  it  in  different  ways. 
Amongst  all  these  converse  phenomena,  the  most  interesting  is 
that  exercised  by  terrestrial  magnetism  on  currents,  and  attempts 
had  frequently  been  made  to  establish  moving  currents,  which, 
when  left  to  themselves,  might  exhibit  all  the  phenomena  of  the 
needle ;  these  experiments,  however,  all  failed,  owing  to  the  ne- 
cessary mobility  not  being  given  to  the  currents.  At  length  all 
these  difficulties  were  overcome  by  an  ingenious  contrivance  of 
Jlmpere,  which  admits  of  being  applied  to  all  currents. 

Fig.  434  represents  two  vertical  brass  columns  secured  to  a 
wooden  stand,  and  having  at 
the  top  two  horizontal  arms, 
terminating  in  the  mercury  cups 
x  and  yy  in  which  the  central 
point  of  one  is  placed  vertically 
below  the  other.  Where  the 
horizontal  arms  appear  to  be  in 
contact,  they  are  separated  by 
insulating  substances ;  when, 
therefore,  the  feet  of  the  co- 
lumns are  brought  in  connec- 
tion with  both  poles  of  the  circuit,  one  of  the  electric  fluids  will 
reach  the  cup  x,  and  the  other  the  cup  y.  One  of  these  cups  may 
be  named  the  positive,  and  the  other  the  negative. 

A  copper  wire,  curved  in  the  manner  shown  in  Figs  435  and 
436,  is  suspended  to  the  cups  x  and  y.  The  wire  ends  are  sepa- 
rated by  an  insulating  substance  where  they  appear  to  be  in  con- 


Fig.  434. 


464 


INFLUENCE    OF    TERRESTRIAL   MAGNETISM. 


tact ;  they  are  curved  at  the  top,  and  provided  with  steel  points, 
which  are  plunged  into  the  cups  x  and  y  (Fig.  434).  The  one 
point  penetrates  to  the  bottom  of  the  cup,  and  rests  upon  a  small 
glass  plate,  while  the  other  point  is  only  just  immersed  in  the 
mercury.  By  this  suspension  the  wire  becomes  very  moveable. 


Fig.  435. 


Fig.  436. 


On  suffering  a  current  to  pass,  the  wire,  after  making  several 
oscillations,  will  place  itself  in  a  definite  position,  to  which  it  will 
invariably  return  if  removed  from  it. 

If  we  turn  the  current,  bringing  the  column,  which  was  pre- 
viously in  connection  with  the  +  pole  of  the  circuit,  into  contact 
with  the  —  pole,  and  vice  versa,  the  wire  will  describe  half  a 
revolution  round  its  vertical  axis  of  rotation  before  it  will  recover 
its  equilibrium.  In  both  positions  of  equilibrium,  the  circle  stands 
in  such  a  manner  that  its  plane  makes  a  right  angle  with  that  of 
the  magnetic  meridian.  Stable  equilibrium  will  be  established 
when  the  positive  current  passes  from  east  to  west  in  the  lower  half 
of  the  circle. 

Very  weak  currents  are  even  directed  by  terrestrial  magnetism, 
and  on  this  principle  rests  the  construction  of  the  apparatus  in 
Fig.  437.  In  a  piece  of  cork,  swimming  in  acidu- 
lated water,  we  secure  a  piece  of  zinc  and  a  piece  of 
copper,  which  reach  into  the  fluid,  and  are  con- 
nected at  the  top  by  a  circular  copper  wire.  When 
placed  upon  the  water,  a  current  will  be  found  wrhich 
passes  from  the  zinc  in  the  water  to  the  copper,  and 
then  through  the  wire,  following  the  direction  indi- 
cated by  the  arrows.  This  current  is  sufficiently  strong  to  be 
directed  by  terrestrial  magnetism,  and  will,  therefore,  so  much  the 
more  be  directed,  attracted,  and  repelled,  by  a  magnet. 

As  a  closed  circular  current,  revolving  round  a  vertical  axis, 


Fig.  437. 


ACTION  OF  GALVANIC  CURRENTS  ON  EACH  OTHER.  465 

places  itself  at  right  angles  with  the  magnetic  meridian,  it  follows 
that  a  combination  of  parallel  circles,  which  are  traversed  in  the 
same  direction,  must  range  themselves  in  like  manner.  Thus,  the 
wire  helix,  seen  in  Fig.  438,  when  suspended  by  Ampere's  stand, 
and  when  traversed  by  a  current,  must 
place  itself  in  such  a  manner  that  its  Flg* 438' 

axis  shall  be  in  the  line  of  the  direction 
of  the  needle  of  decimation. 

It  not  only  follows  from  this,  that  the 
needle  of  declination  may  be  thus  imi- 
tated by  a  wire  helix,  but  also  that  the 
south  pole,  that  is,  the  one  directed  to 
the  north,  is  the  one  on  the  right  side  of  which  lies  the  ascend- 
ing current,  if  we  look  at  it  from  its  present  side.  If  we  look 
at  the  wire  from  a,  we  have  the  ascending  current  to  the  right, 
and  the  descending  one  to  the  left ;  but  if  we  consider  the  wire 
helix  in  the  direction  of  b,  we  shall  have  the  ascending  current  to 
our  left ;  a,  consequently,  is  the  south  pole,  and  must  turn  to  the 
north.  In  like  manner,  we  may  say  that,  if  a  needle  of  declina- 
tion be  placed  in  a  position  of  equilibrium,  the  lower  current  will 
go  from  east  to  west. 

The  board,  to  which  the  different  windings  of  the  wire  helix 
(Fig.  438)  are  secured,  is  made  of  a  non-conducting  substance. 

If  we  bring  a  magnetic  bar  to  the  helices  we  have  been  con- 
sidering, we  may  observe  phenomena  perfectly  similar  to  those 
exhibited  on  bringing  a  magnetic  bar  near  a  needle  of  declination. 
In  fact  all  the  apparatus  hitherto  described  will,  as  we  may  con- 
jecture, be  affected  by  magnetic  bars. 

Reciprocal  Action  of  Galvanic  Currents  on  each  other. — Two 
parallel  currents  always  exercise  an  action  on  each  other,  which 
is  more  or  less  energetic  according  to  their  distance,  intensity  and 
length.  If  we  consider  the  direction  of  the  motion  produced,  we 
shall  find  it  to  be  subjected  to  the  following  simple  law;  two  pa- 
rallel currents  attract  each  other  if  they  move  in  the  same  direction, 
but  repel  each  other  if  their  directions  be  opposite. 

The  above  statement  may  be  proved  by  the  following  appa- 
ratus ;  a  b  c  d  ef  is  a  rectangular  figure  formed  of  copper  wire, 
and  suspended  in  the  mercury  cups  x  and  y.  The  current  as- 
cends through  the  column  *,  traverses  the  wire  figure  in  the  direc- 
tion of  the  arrows,  and  descends  into  the  column  v.  The  current 


466  ACTION  OF  GALVANIC  CURRENTS  ON  EACH  OTHER. 


in  the  column  t,  follows  the  same  direction  as  that  in  the  piece  of 
wire  d  e ;  the  same  is  the  case  with  respect  to  the  current  in  b  c 
and  v.  If  we  remove  the  rectangular  figure  from  the  position 
represented  in  Fig.  439,  it  will  always  return  to  the  same,  owing 
to  d  e  being  attracted  by  t,  and  b  c  by  v. 
If  we  put  the  wire  figure  in  Fig.  439  in  the  place  of  that  sus- 


Fig.  439. 


Fig.  440. 


pended  in  Fig.  440,  the  current  in  the  wire  will  have  an  opposite 
direction  from  that  in  the  succeeding  column,  and  we  shall  ob- 
serve a  repulsion ;  parallel  opposite  currents,  therefore,  repel  each 
other. 

We  call  such  currents  as  are  not  parallel,  cross  currents,  whe- 
ther they  lie  in  the  same  plane,  and  their  directions  intersect  each 
other,  or  whether  they  are  in  different  planes,  and  do  not  intersect 
each  other.  In  the  first  case,  the  crossing  point  is  the  point  in 
which  they  intersect  each  other ;  in  the  second,  it  is  a  point  of  the 
shortest  distance  of  both  currents.  Two  cross  currents  always 
strive  to  range  themselves  parallel  to  each  other,  in  order  to  move 
in  the  same  direction;  or  in  other  words :  attraction  takes  place 
between  the  parts  of  a  current  and  those  which  approach  the  cross- 
ing point,  and  then  again,  between  those  going  from  the  crossing 
point.  Repulsion  occurs  between  a  current  moving  towards  the 
crossing  point,  and  another  moving  away  from  the  same  point. 

If,  for  instance,  a  b  and  c  d  (Fig.  441)  are  two  currents,  whose 
crossing  point  is  r,  attraction  will  take  place  between  the  parts 
a  r  and  c  r,  in  which  the  current  passes  towards  the  crossing 
point,  and  between  the  parts  r  b  and  r  d,  in  which  it  goes  from  the 
crossing  point.  Repulsion  takes  place  between  a  r  and  r  d,  and 
further  between  c  r  and  r  b. 


AMPERE'S    THEORY   OF   MAGNETISM.  467 

The  apparatus  of  which  a  diagonal  section  is  represented  in 
Fig.  442,  and  an  outline  in  Fig.  443,  serve  to  prove  this  proposi- 

Fig.  441.  Fig.  443. 


tion.  Two  semi-circular  channels,  divided  by  insulated  partition 
walls  a  and  6,  are  inserted  in  a  plate  of  wood.  In  the  middle 
point  rises  a  spike,  to  which  is  attached  an  easily  moving  copper 
needle  c  d,  the  extremities  of  which  are  of  iron  and  dip  into  the 
mercury  of  the  channel.  Somewhat  below  this  needle  there  is 
another,  ef,  the  extremities  of  which  are  likewise  dipped  into  the 
mercury,  and  may  be  moved  by  the  hand.  The  current  which 
enters  at  x  passes  into  the  one  channel,  and  then  through  the  two 
needles  into  the  other,  and  passes  out  at  y. 

The  repulsion  is  exhibited  on  placing  the  needles  in  the  posi- 
tion indicated  by  Fig.  443,  and  the  attraction  on  bringing  them 
into  such  a  position,  that  the  angle  e  r  d  may  be  less  than  a  right 
angle. 

Ampere's  Theory  of  Magnetism. — The  principle  of  this  theory 
consists  in  considering  each  molecule  of  a  magnet  surrounded  as 
it  were  by  a  current,  always  circulating  about  it  and  returning 
upon  its  own  course,  which  may  for  the  sake  of  simplicity  be  re- 
garded as  circular.  We  must,  therefore,  according  to  this  theory, 
regard  every  section  at  right  angles  to  the  axis  of  the  magnet  to 
be  somewhat  similar  to  what  we  have  attempted  to  delineate  in 
Fig.  444.  Instead  of  taking  into  account  all  the  elementary  cur- 
rents of  each  diagonal  section,  we  may  suppose  the  latter  to  be 

Fig.  444.  Fig.  445. 


468 


AMPERE'S   THEORY   OF   MAGNETISM. 


Fig.  446. 


encircled  by  one  single  current,  which  is,  as  it  were,  the  resultant 
of  all  the  elementary  currents  of  the  diagonal  section,  and  con- 
sequently we  may  regard  a  magnetic  bar  as  a  system  of  parallelly 
closed  currents,  somewhat  in  the  manner  shown  in  Fig.  445. 

What  we  have  said  here  of  a  magnetic  rod  applies  equally  to  a 
magnetic  needle,  and,  in  short,  to  every  magnet,  let  its  form  be 
what  it  may. 

Let  us  suppose  a  wire  helix  extending  from  m,  Fig.  446,  to 
either  side,  and  traversed  by  the  current  in  the  direction  of  the 
arrows;  if  further  we  assume  this  to  be  cut 
through  at  m,  and  the  two  parts  separated, 
it  follows  from  our  definition  that  there  will 
be  a  south  pole  at  a  and  a  north  pole  at  6, 
for  on  turning  to  the  pole  at  a,  we  shall  have 
the  ascending  current  to  our  right,  while  on 
turning  to  the  pole  at  6,  we  here  have  it  to 
our  left. 

If  we  cut  a  wire  helix  at  right  angles  to 
its  axis,  two  contrary  poles  will  be  formed, 
exactly  as  on  breaking  a  magnet. 

Further,  it  is  clear  that  the  contrary  poles 
a  and  b  attract  each  other,  for  on  looking 
only  at  the  end  circle,  we  see  that  the  cur- 
rents are  directed  parallelly  and  similarly, 
and  the  same  is  the  case  with  respect  to  all  the  other  circles. 

The  best  way  to  give  an  illustration  of  the  attraction  and  re- 
pulsion of  the  poles  in  different  positions  of  the  magnets  with 
respect  to  each  other,  is  by  drawing  arrows  upon  wooden  or 
pasteboard  cylinders  from  1  to  1,5  foot  in  length,  and  from  2  to  3 
inches  in  diameter,  as  seen  in  Fig.  445,  which  represents  the 
direction  of  the  currents ;  further,  we  may,  in  like  manner,  mark 
on  both  cylinders  the  similar  poles,  designating  the  north  pole  as 
+,  for  instance,  and  the  south  pole  as  — .  By  the  help  of  two 
such  models  we  may  easily  show  how  similar  poles  always  repel, 
and  contrary  poles  attract  each  other,  and  in  whatever  manner  we 
bring  them  near  one  another. 

According  to  this  hypothesis,  the  magnetism  of  the  earth  also 
depends  upon  such  currents,  moving  in  the  crust  of  the  earth 
parallel  with  the  magnetic  equator. 


ROTATION    OF   MOVABLE    CURRENTS    AND   MAGNETS.     469 


Fig.  447. 


Fig.  448. 


Rotation  of  Movable  Currents  and  Magnets.  —  Let  abed, 
Fig.  447,  be  the  horizontal  section  of  a  magnet  standing  in  a 
vertical  position,  and  a  vertical  current  appearing  foreshortened 
at  the  point  s,  and  which  we  will  assume  to  be  ascending,  and 
which  is  capable  of  rotating  round  the  vertical  axis 
of  the  magnet;  it  will  then  be  evident  from  the  above 
developed  principles,  that  the  portion  a  b  of  the  mag- 
netic current  will  repel  the  current  s,  while  it  will  be 
attracted  by  b  c,  the  current  s  must  consequently  ro- 
tate in  the  direction  of  the  current  in  the  magnet.  If  the  current 
s  were  descending,  the  rotatory  direction  would  be  reversed ;  in 
like  manner,  of  course,  the  inversion  of  the  magnetic  poles  will 
occasion  the  rotation  to  assume  an  inverse  direction. 

A  rotation  of  this  kind  may  be  effected  by  means  of  the  ap- 
paratus seen  in  448.  To  a  vertical  staff/  is  attached  a  movable 
horizontal  staff  a,  in  such  a  manner 
that  it  may  be  moved  to  any  height 
we  please,  by  means  of  a  screw. 
This  horizontal  staff  is  provided  with 
a  brass  ring,  to  which  is  attached  a 
circular  wooden  channel  for  holding 
mercury.  In  the  brass  ring  there  is 
a  cork  disc,  through  the  middle  of 
which  passes  a  vertical  magnetic 
bar,  having  at  the  top  a  joint  with  a 
steel  cup  screwed  on  it.  This  cup 
has  a  fine  point  in  its  centre,  sup- 
porting a  copper  band  b,  which  is 
curved  at  either  side,  in  such  a 
manner  that  its  lower  ends,  with 
their  platinum  points,  dip  into  the 
mercury.  In  the  middle  of  the 
copper  band  is  a  mercury  cup  p. 
On  the  one  polar  wire  of  the  chain 
being  immersed  in  the  cup  jp,  and 
the  other  in  the  channel,  the  current  passes  through  the  two  arms 
of  the  copper  band,  which  then  begins  to  rotate.  The  action  of 
the  magnet  on  the  current  in  the  one  arm  of  the  band  is  sustained 
by  the  action  which  the  magnet  produces  on  the  current  in  the 
other  arm. 
40 


470  PHENOMENA    OF    INDUCTION. 

We  may  similarly  produce  the  rotation  of  a  movable  magnet 
round  a  fixed  current,  and  the  rotation  of  a  moving  current  round 
a  fixed  magnet ;  and  the  apparatus  serving  for  this  purpose  have 
been  constructed  in  a  variety  of  ways. 


CHAPTER    II. 

PHENOMENA  OF  INDUCTION. 

AN  electric  current  is  able  to  engender  like  electric  currents  in 
another  contiguous  conductor  at  the  moment  of  its  origin  or  its 
cessation,  and  also  by  mere  approximation  or  distance. 

These  phenomena  were  discovered  by  Faraday  in  the  year 
1838,  and  deserve  the  greatest  attention,  both  owing  to  their 
theoretical  importance,  and  to  the  numerous  facts  that  can  be 
derived  from  this  principle.  These  new  currents  produced  in 
conductors  by  the  distributing  action  of  other  currents,  are  termed 
Induction  currents.  They  might  also  be  called  temporary  currents, 
as  they  last  but  a  moment.  If  we  were  to  name  them  according 
to  their  origin,  as  has  been  done  in  the  case  of  the  thermo-electric 
and  the  hydro-electric  currents,  we  might  give  them  the  appellation 
of  magneto-electric,  or  electro-electric,  since  they  are  either  engen- 
dered by  magnetism  or  electricity.  We  will,  however,  once  for 
all,  abide  by  the  term  Induction  currents,  which  has  also  been 
adopted  by  the  majority  of  natural  philosophers. 

Action  of  an  Electric  Current  on  a  Conducting  Circuit  within 
itself. — Two  copper  wires  covered  with  silk  thread  are  wound 
upon  a  reel  of  wood  or  metal  in  the  way  exhibited  in  Fig.  449. 
The  one  wire  runs  beside  the  other  without  there  being  any  com- 
munication   between    them ;     if, 
therefore,   we    close    a   galvanic 
circuit  with  one  wire,  while  we 
place  its  two  ends  a  and  b  in  con- 
nection with  its  poles,  the  current 
will  circulate   through  that  wire 
without   passing  into  the   other. 
In  this  other  wire,  however,  a  cur- 


ACTION   OF   AN   ELECTRIC   CURRENT,   ETC.  471 

rent  in  an  opposite  direction  is  produced  by  the  inductive  action 
of  this  current,  provided  the  ends  c  and  d  of  this  second  wire  are 
in  connection ;  which  may  be  effected  by  means  of  a  multiplicator, 
on  bringing  c  into  communication  with  the  end  of  one  of  the  wires 
of  the  latter,  and  d  with  the  end  of  the  other  wire.  At  the  moment 
in  which  we  close  the  galvanic  circuit  with  the  first  wire,  the 
deviation  of  the  needle  of  the  multiplicator  indicates  a  current  in 
the  adjoining  wire ;  supposing  the  positive  current  to  pass  in  the 
main  wire  from  a  to  6,  the  multiplicator  manifests  that  there  is  a 
current  in  the  contiguous  wire  traversing  it  in  a  direction  from 
d  to  c. 

This  current  in  the  adjoining  wire  is  not,  however,  lasting,  for 
the  needle  of  the  multiplicator  returns  immediately  to  zero  on  the 
graduated  line ;  as  soon  as  the  principal  current  is  interrupted, 
the  needle  of  the  galvanometer  turns  in  the  opposite  direction,  it, 
therefore,  indicates  a  current  passing  through  the  neighboring 
wire  in  the  direction  from  c  to  d,  consequently,  in  the  same  direc- 
tion in  which  the  interrupted  current  had  moved. 

An  electric  current  may,  therefore,  induce  currents  in  a  conti- 
guous wire  both  at  the  moment  of  its  origin  and  of  its  cessation. 
The  current  induced  by  the  closing  of  the  circuit  has  the  opposite 
direction  to  the  one  induced  by  the  interruption  of  the  circuit,  and 
is  in  the  same  direction  as  the  principal  current. 

In  the  above  adduced  experiments,  the  current  in  the  principal 
wire  induced  a  current  in  the  other  wire  both  at  the  moment  of 
its  origin  and  of  its  cessation;  we  might,  therefore,  conjecture 
that  these  actions  were  produced  by  some  modifications  accom- 
panying the  beginning  and  ending  of  the  current.  To  remove 
all  doubt  on  the  subject,  Faraday  has  proved  by  experiment,  that 
exactly  the  same  results  are  obtained  on  bringing  a  conducting 
wire  that  is  traversed  by  a  current,  consequently,  the  wire  from 
which  the  inducing  action  proceeds  nearer  to,  or  further  from  the 
wire  in  which  we  wish  to  induce  a  current. 

If,  therefore,  we  say  that  the  action  of  a  current  on  a  closed 
conductor  begins,  we  either  understand  thereby  that  the  inducing 
current  itself  begins,  or  that  it  is  already  on  its  course,  and  brought 
near  to  the  closed  conductor.  In  these  two  cases  the  actions  are 
precisely  similar.  If  we  say  that  the  action  of  a  current  on  a 
closed  conductor  stops,  it  means,  that  the  inducing  current  itself 
either  ceases,  or  is  removed  from  the  closed  conductor. 


472  ACTION    OF    THE    WINDINGS    ON    EACH    OTHER. 

Currents  of  induction  produce  all  the  actions  of  ordinary  cur- 
rents, as,  for  instance,  shocks  and  sparks.  On  bringing  the  ends 
of  the  wires  c  d  close  together,  we  see  a  spark  pass  over,  if  the 
circuit  be  closed  by  the  ends  a  and  b  of  the  inducing  wire.  If 
we  seize  the  wire  end  c  in  one  hand,  and  d  in  the  other,  (the 
hands  must  be  somewhat  moistened  for  making  the  experiment), 
we  shall  feel,  on  the  opening  and  closing  of  the  principal  current 
a  shock,  the  violence  of  which  will  depend  upon  the  length  of  the 
coiled  wire. 

Very  violent  actions  may  be  produced  on  the  nerves  by  the 
above  described  double  spiral  apparatus,  for  if  the  encircling  wire 
be  of  considerable  length,  the  intensity  of  the  inductive  currents 
will  be  incomparably  stronger  than  those  of  the  current  yielded 
by  the  galvanic  circuit  commonly  used.  A  simple  galvanic  cir- 
cuit, or  even  a  battery  of  4,  6,  or  even  12  pairs  gives  no  shocks 
by  itself,  but  if  we  close  a  circuit  of  a  few  or  only  one  pair,  with 
the  ends  of  the  inducing  wire,  we  shall  obtain  a  powerful  shock 
at  this  wire. 

An  induction  spiral  changes,  therefore,  in  some  degree  the 
electric  quantity  of  a  current  yielded  by  one  or  more  pairs  of 
large  superficies  into  a  current  of  great  intensity;  an  apparatus  of 
this  kind  affords,  therefore,  an  excellent  means  of  producing 
physiological  effects,  if  care  be  taken  alternately  to  close  and 
open  the  circuit  in  rapid  succession.  Many  very  ingenious  con- 
trivances have  been  proposed  for  effecting  this  purpose. 

Action  of  the  Windings  on  each  other. — If  we  close  a  simple 
circuit  by  a  short  wire,  we  shall  obtain  only  a  faint  spark  on  again 
opening  it,  and  no  shock ;  but  if  we  use  a  very  long  wire  instead 
of  the  short  one,  we  shall  see  a  much  stronger  spark  on  opening 
the  circuit,  and  if  we  hold  one  end  of  the  wire  in  one  hand,  and 
the  other  in  the  opposite  hand,  we  shall  perceive  a  shock  at  the 
moment  of  opening  the  circuit.  These  actions  are  very  much 
strengthened  by  winding  the  wire  as  closely 
Fig.  450.^  ag  pOSSibie>  ant[  nere  ^  is?  Of  course,  neces- 
sary to  cover  the  wire  with  silk,  in  order  to 
prevent  the  current  passing  laterally  from 
one  winding  to  another. 

This  action  of  long  spiral  wires  may  be 
well  shown  by  means  of  a  simple  spiral,  Fig. 
450,  it  being  only  necessary  to  plunge  the  wire  ends  m  and  n 


INDUCTION   OF    ELECTRIC    CURRENTS   BY  MAGNETS.     473 

into  the  mercury  cups  forming  the  poles  of  a  galvanic  circuit,  and 
on  withdrawing  the  ends  of  the  wires  we  shall  see  a  brighter  spark 
and  feel  the  shock.  On  suffering  these  shocks  to  pass  in  rapid 
succession  through  the  body,  violent  actions  on  the  nerves  may 
be  induced. 

As  to  what  relates  to  the  explanation  of  these  phenomena,  we 
shall  easily  comprehend  that  they  must  stand  in  a  very  close  re- 
lation to  the  induction  phenomena  before  described.  Faraday 
ascribes  these  effects  to  an  inductive  action  reciprocally  exercised 
on  each  other  by  the  convolutions  of  one  and  the  same  spiral,  and 
calls  this  current  of  induction  an  extra-current.  It  arises  at  the 
moment  of  the  opening  and  closing  of  the  circuit. 

Induction  of  Electric  Currents  by  Magnets. — A  metal  wire,  en- 
circled with  silk,  must  be  wound  over  a  wooden  or  metal  rod,  the 
inner  opening  of  which  is  sufficiently  large  to  admit  of  the  inser- 
tion of  a  magnet.  The  two  ends  m  and  n  of  the  wire  must  be 
put  r.?;o  communication  with  the  two  ends  of  the  multiplicator 
wire  of  a  galvanometer,  sufficiently  far  removed  to  prevent  the 
magnet  from  causing  the  needle  of  the  instrument  to  deviate.  At 
the  moment  in  which  the  magnet  is  inserted  into  the  helix,  we 
shall  observe  a  deviation  of  the  galvanome- 
ter needle,  which,  however,  will  soon  return 
to  the  point  0  of  the  graduated  division, 
moving  away  again,  in  an  opposite  direction, 
on  withdrawing  the  magnet  from  the  helix. 
The  direction  of  the  current,  indicated  by 
the  galvanome^r,  on  the  approximation  of 
the  magnet,  is  opposite  to  that  of  the  cur- 
rents, which,  according  to  Ampere's  theory, 
circulate  about  the  magnet;  the  current, 
induced  in  the  wire,  on  the  removal  of  the 
magnet,  has  the  same  direction  as  these  currents. 

By  this  experiment,  an  action  is  produced  on  the  closed  wire 

coils,  on  the  approximation  or  removal  of  the  magnet ;  but  this 

magnetic  action  may  begin  and  cease  in  a  different  manner;  it 

[may,  for  instance,  begin  at  the  moment  in  which  the  magnetic 

i  fluids  in  the  iron  are  decomposed,  and  cease  when  it  returns  to 

the  non-magnetic  condition.    This  may  be  shown  in  the  following 

manner. 

40* 


474      INDUCTION    OF    ELECTRIC    CURRENTS    BY   MAGNETS. 

In  Fig.  452  a  &  is  a  strong  horse-shoe  magnet,  m  c  n  a  piece  of 
soft  iron,  likewise  bent  in  the  form  of  a 
horse-shoe,  and  having  its  limbs  enclosed 
by  the  coils  of  one  long  wire,  covered  with 
silk.     The  direction  of  the  coils,  on  both 
limbs,  must  be  such  that,  on  the  current 
passing  through  the  wire,  the  two  limbs 
may  form  opposite  poles.     The  two  ends  of 
the  wire  are  connected  together  at  a  sufficient 
distance  from  the  iron  and  the  magnet,  and 
a  simple  magnetic  needle,  above  or  below 
which  the  wire  is  conducted,  is  at  once 
made  to  deviate  by  the  induced  current.     If  we  rapidly  bring  the 
magnet  a  b  to  the  limbs  m  n,  the  needle  will  indicate  the  pre- 
sence of  a  current  having  an  opposite  direction  to  that  which, 
according  to  Jlmpere's  theory,  circulates  round  the  iron  that  has 
now  been  converted  into  a  magnet.    On  the  removal  of  the  mag- 
net a  b,  the  induced  current  takes  the  same  direction  as  the  one 
now  ceasing  in  the  soft  iron. 

We  may  easily  show  that  this  current,  induced  in  the  wire,  is 
not  the  direct  action  of  the  magnetic  poles  of  the  approximated 
magnet;  for  this  current  attains  such  intensity,  that,  if  even  the 
two  ends  of  the  wire  are  not  in  perfect  contact,  but  at  some  little 
distance  from  each  other,  a  vivid  spark  will  pass  over,  as  well 
when  the  magnet  is  rapidly  approximated,  as  when  it  is  removed. 
This  electric  spark  is  evidently  produced  by  magnetic  actions. 
On  taking  one  end  of  the  wire  in  each  hand,  we  experience,  on 
the  approximation  and  removal  of  the  magnet,  a  shock,  which, 
provided  the  magnet  be  sufficiently  powerful,  will  be  like  the 
shock  of  a  small  Leyden  jar. 

Currents  may  even  be  induced  by  terrestrial  magnetism.  If 
we  hold  a  rod  of  soft  iron,  encircled  by  a  wire  helix,  in  the  direc- 
tion of  the  needle  of  inclination,  and  then  suddenly  invert  it,  so 
that  its  upper  part  shall  incline  downward,  and  vice  versa,  a  cur- 
rent will  be  induced  in  the  wire  helix. 

If  the  inner  horse-shoe  of  the  apparatus,  seen  in  Fig.  430, 
rotate  under  the  circumstances  indicated  in  the  experiment  ad- 
duced, currents  must  be  induced  in  the  windings  of  the  wire,  on 
the  approximation  of  the  limbs  of  the  inner  horse-shoe  towards 


MAGNETO-ELECTRIC    MACHINES    OF    ROTATION.  475 

those  of  the  external  iron,  these  currents  will  be,  according  to  the 
above  developed  principles,  opposite  to  those  occasioned  by  the 
rotation;  the  currents,  induced  by  rotation,  must  necessarily 
weaken  the  force  with  which  the  limbs  of  the  two  horse-shoes 
attract  and  repel  each  other;  and  thus,  these  currents  of  induc- 
tion cause  the  mechanical  effect,  produced  by  such  apparatus  of 
rotation,  to  be  much  less  considerable  than  one  might  be  led  to 
expect,  judging  from  the  force  of  magnetism  that  may  be  imparted 
to  a  piece  of  soft  iron  by  a  galvanic  current. 

Magneto -Electric  Machines  of  Rotation. — If  we  suppose  the 
ends  of  the  inductive-spirals,  which  are  at  the  poles  of  the  core  of 
a  horse-shoe  formed  of  a  piece  of  soft  iron,  (as  have  been  consi- 
dered at  page  474,)  to  be  in  connection  with  each  other,  and 
then,  that  this  soft  iron  revolves  rapidly  about  a  vertical  axis,  so 
that  the  pole  m,  which  is  immediately  above  a,  after  half  a  revo- 
lution, stands  above  6,  there  will  then  be  a  current  induced  in  the 
convolutions  of  the  wire,  m  recedes  from  a,  and  n  from  b ;  this 
current  will  now  continue  with  varying  strength,  but  with  unvary- 
ing direction  during  half  a  revolution,  that  is,  while  m  turns  from 
a  to  6,  and  n  from  b  to  a ;  as  soon,  however,  as  the  second  rota- 
tion begins,  the  direction  of  the  current  will  change,  and  will 
again  change  after  the  completion  of  a  whole  rotation ;  if,  there- 
fore, the  soft  iron  rotate  rapidly  with  its  wire  convolutions,  the 
latter  will  be  constantly  traversed  by  alternating  currents  passing 
into  each  other  every  time  the  poles  of  the  soft  iron  stand  over 
the  poles  of  the  magnet.  That  the  direction  of  the  currents 
actually  changes  in  the  way  indicated,  is  easily  seen  from  the 
rules  given  concerning  the  direction  of  the  induced  currents,  for, 
as  a  and  b  are  opposite  poles,  the  removal  of  a  must  induce  a 
current  in  the  same  direction  as  an  approximation  towards  the 
pole  b. 

In  order  to  be  able  conveniently  to  make  experiments  on  the 
currents  induced  by  magnets,  machines  have  been  constructed 
according  to  the  above  indicated  principles,  which  bear  the  name 
of  magneto-electric  machines  of  rotation.  Fig.  453  represents 
one  of  these.  The  inductive  spirals,  A  and  B,  are  wound  round 
two  cylinders  of  soft  iron,  secured  to  the  two  ends  of  a  horizontal 
iron  plate,  the  centre  of  which  is  on  a  vertical  iron  axis,  as  may 
be  seen  in  Fig.  454.  The  manner  in  which  the  rotation  of  this 


476  MAGNETO-ELECTRIC    MACHINES    OF    ROTATION. 

Fig.  453. 


Fig.  454.  vertical  iron  axis  is  effected,  is  made  apparent  in 
Fig.  453,  and  needs  no  further  explanation.  During 
the  rotation  the  two  iron  cores  pass  under  the  poles 
of  several  powerful  horse-shoe  magnets,  laid  hori- 
zontally over  each  other,  and  each  iron  core  of  the 
horse-shoe  is  thus  alternately  converted  into  a  north 
and  a  south  pole. 
The  convolutions  around  both  iron  cores  are,  of  course,  formed 
only  by  one  very  long  piece  of  wire.  The  one  end  is  fastened  by 
means  of  a  screw  to  an  iron  ring  g,  protected  by  some  insulating 
substance,  solid  wood  or  iron,  from  contact  with  the  iron  axis  of 
rotation,  as  seen  in  Fig.  455.  The  opposite  end  of  the  wire  is, 
in  like  manner,  screwed  upon  the  iron  plate  which  supports 
two  cores ;  it  is,  consequently,  in  contact  with  the  whole  iron  axis 
of  rotation. 

On  this  iron  axis  an  iron  cylinder  h  is  immediately  secured, 
which  we  will  at  once  consider.     As  the  iron  ring  g  is  in  com- 


MAGNETO-ELECTRIC    MACHINES    OF    ROTATION.  477 

munication  with  one  end  of  the  wire,  and  the  iron        Fig.  455. 
cylinder  h  with  the  other,  we  may  regard  g  and  h  as 
the  ends  themselves ;    the  inductive  spiral  will  be 
closed  on  bringing  g  and  h  into  connecting  commu- 
nication with  each  other ;  on  this  being  done,  the  current  of  in- 
duction will  circulate  in  the  wire  coils,  and  the  whole  system  be 
made  to  rotate.     For  the  sake  of  simplifying  the  matter,  we  will 
designate  the  whole  rotating  system  by  the  name  of  Inductor. 

We  have  still  to  consider  the  iron  cylinder  A,  which  consists  of 
three  divisions  lying  over  one  another,  and  of  which  only  the 
middle  one  has  a  perfectly  unbroken  circumference.  At  the  upper 
parts  are  two  channel-like  depressions  diametrically  opposite  to 
each  other,  while,  at  the  lower  end  of  h,  a  part  is  cut  away, 
which  takes  off  about  half  the  circumference,  as  may  be  clearly 
seen  in  our  Figure. 

On  either  side  of  the  axis  of  rotation  is  a  small  brass  column 
with  several  apertures,  in  which  metallic  springs  may  be  inserted, 
and  the  circuit  be  thus  closed  in  various  ways. 

Our  Figure  represents  the  machine  as  it  must  be  arranged, 
in  order  to  produce  powerful  physiological  actions.  In  the  upper- 
most aperture  of  the  column  to  the  right,  a  spring  is  screwed  on 
which  constantly  presses  upon  the  iron  ring  g  during  the  rotation 
of  the  inductor ;  but  the  steel  spring  in  the  next  aperture  closes 
upon  the  upper  part  of  the  iron  cylinder  A,  and  in  this  manner 
the  circuit  is  closed ;  while,  as  often  as  the  end  of  the  steel  wire 
passes  over  one  of  the  channel-like  depressions,  the  connection  is 
interrupted.  This  interruption  occurs  exactly  when  the  poles  of 
the  inductors  have  been  removed  from  over  the  magnetic  poles. 
There  exists,  however,  another  connection  between  the  iron  ring 
_  and  the  cylinder  A,  into  which  the  human  body  may  be  brought. 
A  brass  spring,  constantly  pressing  upon  the  middle  part  of  the 
cylinder  A,  is  screwed  into  the  left  side  of  the  brass  pillar ;  by 
which  means  the  small  brass  pillar  to  the  left  is  connected  with 
h,  as  g  is  with  the  pillar  to  the  right.  A  metallic  conductor  L  is 
in  connecting  contact  with  the  pillar  to  the  left,  and  the  conductor 
R  with  the  pillar  to  the  right;  as  often,  therefore,  as  the  current 
there  is  interrupted  by  the  sliding  of  the  steel  spring  over  the  depres- 
sions, the  shock  of  disjunction  will  pass  through  the  body,  for  it 
is  only  then  that  the  electric  current  (which  hitherto  has  passed 
directly  from  h  through  the  steel  spring  to  the  right  hand  pillar) 


478  MAGNETO-ELECTRIC    MACHINES    OF   ROTATION. 

Fig.  456. 


now  passes  by  a  circuitous  course,  first  to  the  left  pillar,  from  this 
to  the  conductor  L,  through  the  human  body  to  R,  and  then  finally 
to  the  pillar  at  the  right.  On  turning  the  machine  rapidly,  the 
shocks  of  disjunction  will  succeed  each  other  so  violently  that  it 
will  scarcely  be  possible  to  endure  the  effect.  If  we  wish  to 
weaken  the  intensity  of  the  shocks,  it  is  only  necessary  to  turn 
the  machine  more  slowly,  or  to  connect  both  poles  of  the  inducing 
magnets,  by  means  of  an  armature  of  soft  iron. 


THERMO-ELECTRIC   CURRENTS,   ETC.  479 


PART  V. 

THERMO-ELECTRIC  CURRENTS  AND  ANIMAL  ELECTRICITY.* 

IF  two  metallic  bars  be  so  soldered  together  that  they  compose 
a  closed  circuit  of  any  form  we  choose  to  give  them,  a  more  or  less 
intense  current  will  be  produced  as  often  as  the  temperature  varies 
at  the  two  places  of  junction,  the  current  continuing  as  long  as  this 
difference  of  temperature  is  maintained. 

This  may  be  shown  for  a  special  case  with  the  apparatus  in 
Fig.  457.  s  s'  is  a  piece  of  bismuth,  s  c  s'  a  band  of  copper  sol- 
dered on  the  ends  of  the  bismuth  bars ;  a  b  is  a  Fi  457 
magnetic  needle,  movable  freely  on  a  point.  If 
the  two  places  of  junction  have  the  same  tempera- 
'ture  as  the  surrounding  air,  the  apparatus  must 
be  so  placed  that  the  plane  s  c  sr  may  coincide 
with  the  plane  of  the  magnetic  meridian,  and  that, 
consequently,  the  needle  may  stand  parallel  with 
the  axis  and  the  longer  sides  of  the  bismuth  bar. 
As  soon,  now,  as  one  of  the  joining-places,  s,  for  instance,  is 
heated,  the  needle  will  experience  a  more  or  less  strongly  marked 
deviation;  but  if  this  spot  s  be  cooled  below  the  temperature  of 
the  surrounding  air,  we  shall  observe  a  deviation  in  the  opposite 
direction. 

These  deviations  of  the  needle,  first  to  the  one  side  and  then  to 
the  other,  evidently  indicate  the  presence  of  an  electric  current, 
traversing  the  apparatus  in  a  definite  direction,  if  the  spot  s  be 
warmer  than  sf ;  but  in  an  opposite  one  if  s  be  cooler  than  sf. 

All  metals  do  not  yield  the  same  marked  results  as  bismuth  and 
copper ;  and  in  such  cases  we  must  use  a  system  of  two  needles, 
as  seen  in  Fig.  458,  instead  of  one.  The  upper  band  s  c  s1  has 

*  Professor  T.  Thomson's  "Heat  and  Electricity,"  8vo.  2d  edition,  London,  1840. 


480 


THERMO-ELECTRIC    CURRENTS,    ETC. 


Fig.  458. 


Fig.  459. 

0 

fa 


Fig.  460. 


an  opening  in  the  middle,  to  admit  of  the  passage  of  the  con- 
necting piece  between  the  two  needles,  while  the 
point,  however,  on  which*  the  system  of  the  two 
needles  plays,  passes  to  the  upper  needle. 

It  is  not  essential  to  have  an  especial  apparatus 
(as  seen  in  Fig.  458)  for  making  the  fundamental 
experiments  on  thermo-electric  currents,  since 
we  may  use  any  delicately  suspended  compass 
needle  destined  for  this  purpose,  somewhat  like 
that  delineated  in  Fig.  459.  Here  we  have  an 
elongated  parallelogram,  Fig.  460,  as  the  thermo-electric  element, 
composed  of  bismuth  and  antimony.  In  our  figure  the  lightly 
shaded  half  designates  the  former,  and  the  darkly  shaded  half  the 
latter  constituent.  The  two  metals  are  soldered  together  at  s  and 
sf.  In  order  to  make  this  experiment,  we  must  carefully  warm, 

over  a  small  spirit 
lamp,  the  one  sol- 
dered junction,  and 
then   hold    one   of 
the  longer  sides  of 
the  figure  over  the 
magnetic      needle, 
which  must  then  be 
in  its  usual  position.     We  must  re- 
mark here,  that  Fig.  460   is  deli- 
neated on  a  somewhat  smaller  scale 
than  459 ;  since  the  parallelogram 
of  bismuth   and  antimony  ought  to 
be  so  large,  that  each  of  its  longer 
sides  may  be  at  least  of  equal  length  with  the  magnetic  needle. 

Simple  thermo-electric  circuits  are  often  made  in  the  manner 
represented  in  Fig.  461 ;  a  b  is  a  small  bar  of  antimony  or  bis- 
muth, at  both  sides  of  which  a  copper 
wire  a  e  d  b  is  soldered.  To  make  this 
experiment,  we  must  warm  the  one  sol- 
dered joining  either  at  a  or  b,  and  hold  the 
piece  of  wire  e  d  over  the  needle. 

The  investigations  that  have  been  made 
as  to  the  mutual  relation  of  different  metals,  with  respect  to  the 
excitement  of  thermo-electric  currents,  have  shown  that  the  metals 


Fig.  461. 


THERMO-ELECTRIC   PILES.  481 

admit  of  being  ranged  in  one  series,  which  has  this  property,  that, 
on  forming  a  circuit  of  every  two  metals,  and  heating  the  place  of 
contact  of  the  two,  the  +  current  at  this  spot  will  pass  from  the 
metal  standing  immediately  below  it  to  the  one  above. 
Antimony  Tin 

Arsenic  Silver 

Iron  Manganese 

Zinc  Cobalt 

Gold  Palladium 

Copper  Platinum 

Brass  Nickel 

Rhodium  Mercury 

Lead  Bismuth 

Thus,  in  the  apparatus,  Fig.  457,  the  current  will  pass  in  the 
direction  from  s  over  c  to  sf,  and  then  back  to  s  on  heating  the 
soldered  part  at  s.  At  this  point  s,  therefore,  the  next  body 
standing  higher,  viz.,  copper,  is  positive  with  respect  to  the  lower 
one,  bismuth.  In  the  parallelogram,  Fig.  460,  the  positive  cur- 
rent circulates  in  the  direction  of  the  arrow,  if  the  spot  at  s  is 
warmer. 

Thermo-electric  Piles. — As  in  the  case  of  Volta's  piles,  so  we 
may  also  here  combine  many  thermo-electric  elements  to  form 
thermo-electric  piles,  capable  of  giving  a  current  if  the  soldered 
parts  1,  3,  5,  &c.,  be  warmed,  while  the  intervening  points  re- 
main cold. 

Thermo-electric  piles  of  this  kind  may  serve,  in  connection 
with  multiplicators,  to  make  the  slightest  difference  of  tempera- 
ture manifest.  Amongst  all  those  constructed 
for  this  purpose,  the  apparatus  proposed  by 
Mobile  is  undeniably  the  most  ingenious,  and 
the  most  sensitive.  Fig.  462  represents  an 
apparatus  of  this  kind.  It  is  composed  of 
from  25  to  30  very  fine  needles  of  bismuth 
and  antimony,  which  are  about  4  or  5  centi- 
metres in  length.  They  are  so  soldered  Fig' 463' 
together,  see  Fig.  463,  that  all  the  even 
soldered  joinings  are  on  one  side,  and  the  odd 
joinings  on  the  other.  The  whole  forms  a 
small,  compact,  solid  bundle,  owing  to  the  insulating  substances 
with  which  the  intervals  between  the  several  rods  are  filled ;  for 
41 


482 


ANIMAL    ELECTRICITY. 


they  must,  of  course,  not  be  in  contact,  excepting  at  the  soldered 
joinings.  One  of  the  two  half  elements  in  which  the  circuit  ter- 
minates is  in  connection  with  the  peg  x9  and  the  other,  with  the 
peg  y,  x  and  y  form  in  this  manner  the  two  poles  of  the  pile,  and 
are  brought  into  communication  with  the  ends  of  the  multipli- 
cator  wire. 

If  the  soldered  points  on  the  one  side  experience  the  slightest 
elevation  of  temperature,  the  multiplicator  needle  will  at  once 
deviate  from  the  magnetic  meridian. 

Animal  Electricity. — It  has  been  long  known  that  there  are 
fishes  capable  of  imparting  electric  shocks;  among  which,  the  most 
remarkable,  are  the  torpedo  and  the  electric  eel.  The  former 
is  met  with  in  the  Mediterranean  and  in  the  Atlantic  Ocean,  and 
the  latter  only  in  the  inland  pools  of  South  America. 

When  the  torpedo  is  out  of  water,  we  experience  a  shock  on 
touching  any  part  of  its  skin,  either  with  the  finger  or  the  whole 
hand. 

We  may,  in  like  manner,  receive  a  shock  on  touching  the  fish 
with  a  good  conductor,  as  that  of  a  metal  rod  several  feet  in  length. 

The  shock  is  prevented  by  every 
bad  conductor,  and  we  may,  conse- 
quently, seize  the  animal  with  impu- 
nity by  means  of  a  glass  or  resin  hook. 
The  back  of  the  animal  is  positively, 
and  the  abdomen  negatively  electric ; 
the  electric  current  passing  through  a 
conducting  wire,  and  connecting  the 
back  and  abdomen,  produces  all  the 
actions  of  electric  currents,  although 
only  in  a  modified  form. 

The  organ  in  which  the  electricity  is 
developed  has,  in  the  different  electric 
fishes,  essentially  the  same  texture  and 
appearance,  although  its  form,  size  and 
arrangement  differ.  We  will  now  at- 
tempt to  give  an  idea  of  the  organ  of 
the  torpedo — the  fish  which  has  been 
most  accurately  examined. 

Fig.  464  represents  a  torpedo  seen 
from  above,  opened  at  the  side  to  show 


Fig.  464. 


ANIMAL    ELECTRICITY.  483 

the  electric  organ.  This  passes  anteriorly  close  to  the  fore  part 
of  the  head,  its  upper  surface  touching  the  skin  of  the  back  by 
means  of  a  fibrous  membrane,  and  the  lower  surface  touching  that 
of  the  abdomen ;  its  external  surface  rests  upon  the  muscle  of  the 
lateral  fin,  and  the  inner  one  at  the  principal  muscle  of  the  head 
and  the  anterior  part  of  the  trunk.  Seen  from  above  or  below, 
the  electric  organ  exhibits  polygonal,  or  roundish  divisions  (Fig. 
465) ;  but,  from  a  lateral  point  of  view,  it  exhibits  parallel  stripes 
or  bands,  as  seen  in  Fig.  466. 

Fig.  465.  Fig.  466. 

The  whole  organ  consists  of  a 
number  of  polygonal,  or  round- 
ish columns,  the  axis  of  which 
runs  in  a  direction  from  the  abdo- 
men to  the  back.  The  marginal 
edge  of  each  column  forms  a  somewhat  thick  tendinous  mem- 
brane, appearing  to  answer  the  same  purpose  as  the  glass  plates 
between  which  the  galvanic  pile  is  built  up.  Each  column  con- 
sists of  a  number  of  fine  tenias,  which  are  either  plane,  or  curved, 
and  are  separated  by  very  adhesive  mucous  layers ;  thus  these 
columns  afford  a  striking  resemblance  in  their  construction  to  a 
galvanic  pile. 

There  are  generally  found  to  be  from  400  to  500  such  columns 
or  piles  on  either  side  of  a  torpedo. 

In  the  electric  eel  (Fig.  467),  the  electric  organ  is  situated  in  its 

Fig.  467. 


tail.  In  this  animal  the  anus  lies  so  far  forward,  that  the  tail  of 
the  gymnotus  is  nearly  4J  times  as  long  as  the  body  and  head 
combined ;  and  here  the  electric  organ  extends  almost  the  whole 
length  of  the  tail  on  either  side  of  and  under  it,  so  that  the  electric 
apparatus  of  the  animal  has  a  very  great  extension,  owing  to  which 
the  electric  eel  is  able  to  impart  shocks  of  extreme  violence. 

In  the  gymnotus,  the  columns  forming  the  electric  organ  do  not 
lie  vertically,  as  in  the  torpedo,  but  extend  in  the  direction  of  the 
tail ;  so  that  the  discs  of  which  they  are  composed  stand  vertically. 


484  ANIMAL    ELECTRICITY. 

Hence  it  comes,  that,  in  the  electric  eel,  the  positive  current  goes 
in  the  direction  of  the  head  towards  the  tail;  consequently,  not 
like  the  torpedo,  where  the  current  passes  from  the  back  to  the 
abdomen. 

Electric  currents,  not  occasioned  by  especial  electric  organs, 
have  been  observed  in  the  animal  organism.  Nobili  has  found, 
that,  on  touching  with  the  one  wire  end  of  a  multiplicator  the  head 
of  a  living  or  dead  frog,  and  its  feet  with  the  other  wire,  a  current 
will  pass  from  the  head  to  the  feet.  In  like  manner,  a  current 
may  be  observed  on  making  an  incision  into  the  muscle  of  any 
animal,  and  connecting  the  exterior  surface  of  the  muscle  with 
the  cut  surface  by  means  of  the  multiplicator. 


OF   HEAT.  485 


SECTION   VII 

OF  HEAT.* 


CHAPTER    I. 

EXPANSION. 

OUR  capacity  of  feeling  enables  us  to  discriminate  between  the 
different  conditions  which  we  term  hot,  warm,  cold,  &c.,  in  various 
bodies.  If  a  body  that  we  call  cold  become  warm,  and  hot,  it 
will  increase  in  volume,  or  be  expanded. 

The  unknown  cause  producing  this  expansion  of  bodies,  and 
which,  at  the  same  time,  occasions  the  different  above-mentioned 
impressions  on  our  capability  of  feeling,  is  termed  heat. 

Heat  not  only  effects  an  expansion  in  bodies,  but  is  likewise 
able  to  alter  their  aggregate  conditions,  fusing  solid,  and  evapo- 
rizing  fluid  bodies.  We  will  now  proceed  to  the  consideration  of 
the  laws  of  these  phenomena. 

The  Thermometer. — Since  all  bodies  are  expanded  by  heat,  and 
as  the  volume  of  a  body  depends  upon  the  degree  of  heat  it 
possesses,  the  expansion  of  a  body  may  serve  to  measure  the 
degree  of  its  heat;  and  this  degree  of  heat  we  term  tem- 
perature, and  the  instrument  used  to  define  it,  a  ther-      lg'^ 
mometer. 

Fig.  468  represents  a  mercurial  thermometer;  the 
bulb  is  filled  with  mercury;  this  fluid  rises  in  the  tube  to 
a  definite  height,  dependent  on  the  temperature.  If  the 
bulb  be  warmed,  the  volume  of  the  mercury  will  be  in- 
creased, and  it  will  rise  in  the  tube,  and  we  say  the  tem- 
perature has  increased.  If  the  bulb  be  cooled,  the 
volume  of  the  mercury  will  again  diminish,  and  the  fluid 
will  sink  in  the  tube,  and  we  say  that  the  temperature 
has  fallen. 

*  See  Professor  Thompson's  "Heat  and  Electricity,"  2d  edition,  8vo.  1840. 

41* 


486  THE   THERMOMETER. 

At  equal  degrees  of  temperature,  the  top  of  the  mercury  will 
always  occupy  the  same  place  in  the  tube ;  thus,  on  comparing 
a  larger  or  a  smaller  thermometer  with  the  first,  both  will  rise  and 
fall  together,  but  the  actual  amount  of  the  rising  and  falling  may 
be  very  different.  If,  for  instance,  the  two  bulbs  are  equal,  but 
the  tube  of  the  one  10  times  larger  in  its  bore  than  that  of  the 
other,  the  mercury  will,  at  an  equal  degree  of  temperature,  rise 
10  times  higher  in  the  narrower  tube. 

A  thermometer  of  this  kind  can  only  serve  to  show  whether  a 
certain  degree  of  temperature  be  present,  or  whether  it  be  higher 
or  lower,  according  as  the  top  of  the  mercury  stands  higher  or 
lower  in  the  tube.  Such  an  instrument  might  be  of  some  use  to 
science ;  but  it  is  only  by  their  graduation  that  thermometers  can 
be  rendered  practically  useful :  thus  enabling  us  to  express  the 
temperatures,  to  compare  them,  and  thus  ascertain  the  laws  of 
heat. 

It  will  of  course  be  understood  that  only  such  glass  tubes  must 
be  applied  to  thermometers  as  are  perfectly  cylindrical;  and 
whether  they  are  so,  is  known  by  observing  if  a  globule  of  mer- 
cary  suffered  to  pass  up  and  down  one  of  these  tubes  occupy  an 
equal  length  in  all  parts  of  the  tube. 

After  a  tube  has  been  blown  out  into  a  bulb,  it  must  be  filled 
.     469  with    mercury ;   for  this  purpose   the  bulb  is 

warmed,  in  order  that  the  air  contained  within 
it  may  be  expanded,  and  then  the  open  end  of 
the  tube  is  rapidly  plunged  into  the  mercury 
(Fig.  469).  On  the  bulb  cooling,  the  mercury 
ascends  into  the  tube.  It  is  sufficient  here,  if 
only  a  few  drops  reach  the  bulb.  If  we  now 
again  invert  the  instrument,  and  heat  the  ball 
a  second  time  till  the  fluid  begins  to  boil,  the 
vapor  of  the  mercury  will  soon  fill  the  whole 
space,  driving  the  air  entirely  out ;  and  when 
the  open  end  of  the  tube  is  again  quickly 
plunged  into  the  mercury,  we  may  be  sure  of  the  bulb  becoming 
entirely  filled. 

Before  the  thermometer  is  closed,  it  must  be  regulated  ;  that  is 
to  say,  as  much  mercury  must  be  added  or  taken  away,  as  is 
necessary  to  make  the  amount  correspond  to  the  medium  tern- 


THE   THERMOMETER. 


487 


Fig.  470. 


Fig.  471. 


perature,  for  which  the  thermometer  is  intended;  it  must  then  be 
hermetically  closed. 

The  graduation  of  thermometers  consists  in  marking  two  fixed 
points  on  the  tube,  and  then  dividing  the  intervening  space  into 
equal  parts.  For  these  points,  the  boiling  and  freezing  points  of 
water  are  generally  taken.  To  determine  the  latter,  the  thermo- 
meter ball  and  the  tube,  as  far  as  it  is  filled  by  the  mercury,  are 
plunged  into  a  vessel  filled  with 
finely  pounded  ice,  (Fig.  470.)  If  the 
temperature  of  the  surrounding  air  be 
higher  than  the  freezing  point,  the  ice 
will  melt,  and  the  whole  mass  will 
assume  the  fixed  temperature  of  the 
freezing  point.  The  thermometer 
will  also  soon  acquire  this  tempera- 
ture, and  from  that  moment  it  will 
remain  perfectly  stationary,  when  we 
have  only  to  mark,  with  accuracy, 
the  point  of  the  tube  where  the  top 
of  the  column  of  mercury  stands.  This  ppint  is  first  designated 
by  a  line  of  ink,  and  subsequently  marked  by  a  diamond. 

In  order  to  determine  the  boiling  point,  we  take  a  vessel  with 
a  long  neck,  (Fig.  471,)  and  heat  distilled  water  within  it  to  the 
boiling  point ;  after  the  boiling  has  gone  on  some  time,  all  parts 
of  the  vessel  will  be  equally  heated,  and  the  vapor  will  escape 
at  the  lateral  openings  ;  the  thermometer  is  then  surrounded  on  all 
sides  by  vapor,  the  temperature  of  which  will  be  the  same  as 
that  of  the  upper  layer  of  water.  The  mercury  will  soon  rise  to 
a  point  at  which  it  will  remain  standing,  and  which  it  will  not 
exceed.  This  point  is  designated  as  100°  C.  (212°  F.)  If  at 
this  moment  the  height  of  the  barometer  be  not  exactly  760mm 
(30  inches),  a  correction  must  be  made,  the  amount  of  which  will 
be  given  when  we  treat  more  fully  of  boiling.  In  the  centigrade 
thermometers  the  interval  between  the  two  fixed  points  is  divided 
into  100  parts,  and  the  thermometer  scale  thus  made.  * 

All  thermometers  constructed  in  this  manner  are  comparable 
instruments ;  that  is  to  say,  they  exhibit  an  equal  number  of  de- 
grees at  equal  temperatures. 

Mercurial  thermometers  may  be  constructed,  which  go  to  the 
600th  F.  degree ;  but  beyond  this  it  is  not  expedient  to  raise  them, 


488  THE    THERMOMETER. 

for  fear  of  approaching  too  nearly  to  the  boiling  point  of  mercury, 
which  is  644°  F.  Below  zero,  the  graduations  of  mercurial  ther- 
mometers may  go  correctly  as  far  as  —  30°  F.  or —  32°  F.;  but 
beyond  this  we  should  approach  too  nearly  to  —  39°  F.,  the 
freezing  point  of  mercury.  As  we  approximate  to  the  tempera- 
tures in  which  bodies  change  their  aggregate  condition,  their  ex- 
pansion is  no  longer  regular. 

All  thermometers  are  not  graduated  according  to  the  centigrade 
scale.  In  Germany  and  France  Reaumur's  thermometers  are  much 
used,  which  are  divided  into  80°,  although  for  scientific  investiga- 
tions the  centigrade  division  of  Celsius  is  almost  exclusively 
applied  to  thermometers. 

It  is,  however,  easy  to  reduce  Celsius'  scale  to  that  of  Reaumur, 
and  vice  versa;  for  as 

100°  C.  =  80°  R.,  1°  C.  =  0,8°  R.,  and  1°  R.  ==  1,25°  C. 

Consequently  x°  C.  =  x,  0,8°  R.,  and  n°  R.  =  n  .  2,25°  C. 
We  may  thus  express  the  same  thing  in  words :  In  order  to  change 
Reaumur's  scale  to  that  of  Celsius,  we  multiply  the  number  of 
the  Reaumur  scale  by  1,25,  or  by  fths.  If,  on  the  other  hand, 
we  want  to  change  Celsius'  degrees  into  the  Reaumur  scale,  we 
multiply  the  given  number  of  the  degrees  by  0,8,  or,  what  is  the 
same,  by  |ths. 

In  England  Fahrenheit's  scale  is  exclusively  made  use  of,  the 
0  of  which  does  not  correspond  with  those  of  the  two  above-men- 
tioned scales.  The  null  point,  or  0  of  Fahrenheit's  thermometer, 
agrees  with  the  graduated  line  —  17|ths  of  Celsius.  Its  melting 
point  for  ice  is  32°,  and  the  boiling  point  of  water  at  212° ;  so 
that  the  interval  between  the  two  is  divided  into  180  degrees. 
According,  therefore,  to  their  absolute  value,  180°  F.  =  100°  C. ; 
consequently  1°  F.  =  f°ths  C.,  and  1°  C.  =  f  °ths  F. 

It  is  necessary,  however,  before  we  attempt  to  reduce  the  de- 
grees of  one  of  these  thermometers  to  the  scales  of  the  others,  to 
take  in-to  account  that  their  zero  points  do  not  coincide.  On 
changing  Fahrenheit's  scale  into  that  of  the  Celsian  thermometer, 
we  must  subtract  32  from  the  given  fundamental  number,  and 
multiply  the  remainder  by  f :  thus  we  have  x°  F.  =  (x —  32)£° 
C.  On  changing  the  Celsius  or  centigrade  scale  into  that  of 
Fahrenheit,  we  multiply  it  by  f ,  and  add  32  to  the  product ;  con- 
sequently y°  C.  =  (y  .  |  +  32)°  F.  In  order  to  facilitate  a 
comparison  of  the  different  scales,  we  give  the  following  table. 


EXPANSION   OF   SOLID   BODIES. 


489 


Celsius. 

Reaumur. 

Fahrenheit. 

—  20 

—  16 

—    4 

—  10 

—    8 

+  14 

0 

0 

32 

+  10 

+    8 

50 

20 

16 

68 

30 

24 

86 

40 

32 

104 

50 

40 

122 

60 

48 

140 

70 

56 

158 

80 

64 

176 

90 

72 

194 

100 

80 

212 

Expansion  of  Solid  Bodies.— As  the  expansion  of  solid  bodies 
by  heat  is  inconsiderable,  means  must  be  devised  for  making  it 
more  apparent  to  the  eye.     This  is  most  simply  effected  in  the 
following  way.     A  rod  b  V  (Fig.  472)  made  of  the  body  to  be 
examined,   is     sup- 
ported  at    one    ex-  Fig.  472. 
tremity  against  a  firm                 ^<^^  & 
obstacle  //',  whilst 
its  other    extremity 
rests     against     the 
shorter   arm    of    an 
angular  lever,  I  c  I', 
that  can  rotate  round 
the  fixed  point  c.  If, 
now,  the  end  /  of  the  shorter  arm  be  pushed  onward  by  the  ex- 
pansion of  the  rod  b  b'y  the  other  end  V  will  traverse  a  much  wider 
space;  and  we  may  in  this  manner  make  even  the  slightest  pro- 
longation of  the  rod  b  bf  perceptible,  provided  the  length  c  I'  be 
very  large  in  proportion  to  c  I. 

By  aid  of  apparatus,  the  construction  of  which  essentially  rests 
upon  the  above-mentioned  principles,  the  expansion  of  many  bo- 
dies has  been  ascertained.  The  following  list  will  give  a  few  of 
the  most  important  of  these. 

For  an  elevation  of  temperature  from  32°  to  212°  F.,  we  have 
these  expansions: 


490  EXPANSION    OF    SOLID    BODIES. 

Platinum  .         .         .     about  0,00086  or  TTVT 

Glass  on  the  average        .         "  0,00087  "  jrW 

Steel  (hard)  .         .         .        "  0,00124  "  ¥£T 

Iron  «  0,00122  "T}r 

Copper  «  0,00171  «  71T 

Tin        .  ..."  0,00217  "  Tfr 

Lead  "  0,00285  «  3|T 

Zinc      .  .         .         .         <•  0,00294  "  *JT 

A  steel  rod,  therefore,  which,  at  32°  F.,  has  a  length  of  807 
lines,  will  have  a  length  of  808  lines  at  212°  F. ;  a  zinc  rod  of 
only  340  lines  in  length  will  expand  1  line  at  an  increase  of  tem- 
perature from  32°  to  212°  F.  Amongst  all  the  above  given 
bodies,  platinum  expands  the  least,  and  zinc  the  most. 

Almost  all  solid  bodies  expand  equally  between  32°  and  212° 
F.,  that  is,  their  expansion  is  proportional  to  the  elevation  of  tem- 
perature. At  an  increase  of  temperature  from  32°  to  50°  F., 
copper  expands  0,000171  ;  at  an  elevation  of  temperature  from 
32°  to  34°  F.,  it  expands  0,0000171  of  its  length  at  32°. 

The  number  expressing  the  extent  of  length  from  32°,  which 
a  body  expands  at  an  elevation  of  temperature  from  32°  to  212°, 
is  termed  the  coefficient  of  the  expansion  of  length.  The  above 
table  gives  the  coefficients  for  platinum,  glass,  steel,  &c. 

Cubic  expansion  is  the  increase  in  the  volume  of  a  body  pro- 
duced by  an  elevation  of  temperature.  Here,  too,  the  volume  of 
the  body  at  32°  is  taken  as  the  starting  point,  and,  by  the  coeffi- 
cience  of  expansion,  we  here  understand  the  number  giving  the 
quantity  which  expresses  by  how  much  of  its  original  volume  at 
32°  a  body,  on  heating  it  to  212°,  expands.  If  we  say,  that  the 
coefficient  of  the  expansion  of  mercury  is  0,018,  it  means  that 
mercury  expands  at  an  elevation  of  temperature  of  212°  about 

1 8 

of  its  volume  at  32°.  If  we  know  the  coefficients  of  ex- 
pansion, and  the  volume  of  a  body  at  32°,  we  may  reckon  its 
volume  at  any  degree  of  temperature,  provided  that  the  expansion 
of  the  body  be  regular  up  to  this  degree  of  temperature. 

In  liquid  and  gaseous  bodies,  the  expansion  can  be  determined 
directly  by  experiments,  whilst,  in  solid  bodies,  it  must  be  esti- 
mated from  the  linear  expansion  observed. 


THE    CO-EFFICIENT    OF    EXPANSION   OF    SOLID   BODIES.   491 

The  coefficient  of  expansion  of  solid  bodies  is  three  times  as  great 
as  the  coefficient  for  the  linear  expansion  of  the  bodies. 

We  may  convince  ourselves  of  this  by  the  following  reasoning. 
Let  /  be  the  side  of  a  cube  at  32°,  then  Z3  is  its  volume,  which  we 
will  designate  by  v\  if  the  cube  be  heated  to  the  212°,  each  side 
becomes  I  (I  -f  r);  consequently  the  contents  of  the  cube  are: 
v'  =  I3  (1  +  r)3  =  I3  (1  +  3  r  +  3  r2  +  r3). 

But  as  r  is  a  very  small  quantity,  we  may  disregard  its  higher 
powers,  when  the  value  of  vf  will,  consequently,  be  reduced  to 

v'  =  I3  (1  +  3  r)  =  v  (1  +  3  r). 

The  volume  v  is,  consequently,  increased  about  3  r  v ;  and  the 
coefficient  of  expansion  for  the  volume  is,  consequently,  3  r. 

We  will  endeavor  to  make  this  more  apparent  by  a  geometrical 
figure. 

Let  a  b  c  be  a  cube  formed  of  a  solid  body  at  32°  (Fig.  473). 
If  this  cube  were  only  expanded  upwards,  at  an  elevation  of  tem- 
perature of  212°,  its  volume  would  increase  as  much  as  the 
quadratic  plate  a  d  c  b,  whose  solid  contents  are  v  r,  if  v  be  the 
volume  of  the  original  die,  and  r  the  linear  coefficient  of  expan- 
sion. If  the  cube  only  expanded  towards  the  left  side,  it  would 
be  increased  by  an  equally  large  plate 
c g  bfj  and,  finally,  a  third  plate  bihc, 
whose  contents  are  likewise  r  v,  would 
be  the  result  of  the  expansion  of  the 
body  anteriorly.  The  cubic  contents  of 
these  three  plates  together  are  3  r  v. 
To  complete  the  estimation  of  the  in- 
crease by  heat  of  the  cube,  we  ought  to 
add  the  contents  of  the  corners,  which 
are  filled  up  at  the  places  where  every 

two  of  the  above-mentioned  plates  meet  together  at  the  edges; 
but  the  amount  of  this  is  so  inconsiderable,  that  it  may  be  dis- 
regarded, since  the  size  of  the  linear  expansion  d  a  is  very  small 
in  comparison  with  the  lengths  of  the  sides  of  the  original  cube, 
and  we  may  thus,  without  serious  error,  assume  3  r  v  to  be  the 
whole  increase  of  the  volume. 

The  coefficient  for  the  expansion  of  length  in  glass,  for  instance, 
is  0,00087,  at  an  elevation  of  temperature  from  32°  to  212°;  con- 
sequently a  mass  of  glass  will  expand  about  0,00251  of  its  volume ; 
the  same  is  the  case  with  the  contents  of  a  glass  vessel.  If  a  glass 


492  EXPANSION   OF   FLUIDS. 

vessel,  at  a  temperature  of  32°,  contains  exactly  1000  cubic  cen- 
timetres, its  contents  will  at  212°  have  increased  to  1002,51  cubic 
centimetres. 

Expansion  of  Fluids. — The  apparatus  in  Fig.  474  may  be  used 
to  determine  the  expansion  of  various  fluid  bodies.  The  neck  of 
a  glass  vessel  of  corresponding  size  is  so  much  contracted  at  one 
spot,  that  the  part  above  may  be,  in  some  degree,  considered  as 
a  funnel.  The  narrowest  part  of  the  neck  a  is  marked  in  some 
way.  The  globe  is  now  filled  with  the  fluid  to  be  examined,  so 
that  it  reaches  above  a,  within  the  funnel,  and 
the  whole  is  cooled  down  to  32°,  while  the  appa- 
ratus is  entirely  surrounded  with  melting  snow, 
or  ice.  When  the  fluid  is  cooled  to  32°,  all  the 
fluid  standing  above  the  mark  must  be  removed. 
If  we  weigh  the  filled  globe,  abstracting  from  the 
weight  found,  that  of  the  glass  vessel,  we  shall 
obtain  the  weight  of  the  fluid,  rising  in  the  globe, 
at  32°.  As  soon  as  the  globe  is  warmed,  the 
fluid  will  expand,  ascending  above  the  mark  a  on 
the  funnel.  When  we  have  warmed  it  to  a  certain  degree  of 
temperature,  as  212°,  we  must  remove  all  the  fluid  standing  above 
a,  and  weigh  it  a  second  time.  After  this,  it  will  be  easy  to  cal- 
culate the  apparent  expansion. 

The  expansion  thus  determined  is,  as  we  have  already  remarked, 
only  the  apparent  one ;  the  true  expansion  of  fluids  being  only 
found  on  adding  the  increase,  by  heat,  of  the  contents  of  the  glass 
vessel  to  the  apparent  expansion. 

At  an  elevation  of  temperature  from  32°  to  212°,  the  expansion 
of  the  volume  at  32°,  is  as  follows: 

Mercury  .  .  .  about  0,018 
Water  ...  "  0,045 

Spirits  of  wine      .         .  "     0,100 

Oil       ....  "     0,100  nearly. 

[Mr.  Dalton  has  given  somewhat  different  estimates  as  the 
results  of  his  experiments  on  these  bodies. 

Mercury  ....  0,0200 
Water  ....  0,0466 
Alcohol  .  .  .  .  0,1100 
Fixed  oils  .  .  .  0,0800 

Oil  of  turpentine          .         .        0,0700  ] 


EXPANSION    OF    GASES.  493 

As  we  see,  the  expansion  by  heat  is  very  considerable  in  the 
case  of  spirits  of  wine  and  oil,  a  circumstance  that  ought  to  be 
attended  to  in  commerce. 

Most  fluids  do  not  expand  regularly  between  32°  and  212°. 
This  is  best  seen  by  constructing  thermometers  of  different  fluids, 
and  comparing  them  with  one  of  mercury.  If,  for  instance,  we 
heat  a  water  thermometer,  which  has  long  been  exposed  to  a  tem- 
perature of  32°,  it  will  not  immediately  rise,  but  will  first  sink, 
and  only  begin  to  rise  when  the  temperature  has  been  raised  to 
42°.  If  we  take  into  account  the  expansion  of  the  glass,  it  will 
be  found  that  water  has  a  maximum  density  at  about  40°,  that 
is,  at  40°  water  is  denser  than  at  any  other  temperature.  Water 
of  40°  will  expand  whether  we  heat  or  cool  it. 

Spirits  of  wine  do  not  expand  regularly,  on  which  account,  a 
spirit  thermometer  does  not,  at  all  temperatures,  correspond  with 
one  of  mercury. 

Expansion  of  Gases. — Gases  expand  by  heat  far  more  than 
solid  and  fluid  bodies,  and  their  coefficients  of  expansion  are  the 
same  for  all  temperatures ;  further,  gases  always  expand  in  pro- 
portion to  the  elevation  of  temperature. 

At  an  elevation  from  32°  to  212°,  the  expansion  of  gases 
amounts  to  0,365  of  their  volume  at  32°. 

Different  methods  have  been  used  to  ascertain  the  coefficients 
of  expansion  for  gases,  amongst  which,  however,  the  following  is 
the  most  simple.  A  glass  bulb  is  blown  at  the  one  end  of  a  thin 
glass  tube,  as  seen  in  Fig.  475,  while  the  other  end  is  drawn  to 
a  fine  point.  On  immersing  the  bulb  in  boiling  F.  4?5 
water,  in  such  a  manner,  of  course,  that  the 
point  shall  project  tolerably  far  beyond  the  fluid, 
the  air  within  it  will  soon  be  heated  to  212°, 
and,  in  consequence  of  this,  will  partially  escape 
from  the  ball.  The  point  must  now  be  closed 
over  a  spirit  lamp,  and  the  bulb  suffered  to  cool 
gradually;  when  it  has  become  quite  cold,  we 
must  then  invert  it,  put  the  point  into  the  mer- 
cury, and  break  it  off;  the  mercury  will  now 
naturally  force  its  way  into  the  ball,  because 
the  air  within  has  been  rarefied  by  the  previous 
heating. 
42 


494  CHANGE    OF    THE    STATE    OF    AGGREGATION. 

If  we  cool  the  ball  to  32°,  by  means  of  melted  snow  laid  upon 
it,  the  mercury,  forcing  its  way  in,  will  exactly  fill  the  space  in 
which  the  air,  remaining  in  the  bulb,  has  expanded  at  an  eleva- 
tion of  temperature  from  32°  to  212°.  If  we  determine,  by 
weight,  the  quantity  of  mercury  that  has  entered,  we  shall  obtain 
the  weight  of  the  amount  of  mercury  which  the  whole  bulb  is 
capable  of  containing ;  and  thus,  consequently,  we  may  calculate 
the  coefficients  of  expansion  of  air. 


CHAPTER   II. 

CHANGE  OF  THE  STATE  OF  AGGREGATION. 

Fusion. — We  may  easily  see  that  fusion,  that  is,  the  transition 
of  a  body  from  the  solid  to  the  fluid  condition,  must  be  a  pheno- 
menon of  heat,  and  that  no  other  power  in  nature,  but  this,  is 
capable  of  producing  a  similar  effect.  We  may  break  ice  and 
reduce  it  to  powder,  and  we  may  expend  every  mechanical  power 
upon  it;  but  yet  it  will  not  be  converted  into  water  until  acted 
upon  by  heat.  The  same  is  the  case  with  lead,  wax,  &c. 
Whether  a  body  be  solid  or  fluid,  depends,  therefore,  entirely  and 
solely  on  its  temperature.  At  any  other  distance  from  the  sun, 
than  the  one  occupied  by  it,  the  earth  would  present  a  very  dif- 
ferent aspect ;  at  a  greater  approximation  to  that  luminary,  most 
metals  would  be  in  a  constant  state  of  fusion,  while,  at  a  greater 
distance  from  it,  the  sea  would  be  a  solid  mass;  there  would  be 
no  running  water,  and,  probably,  no  fluid,  on  the  circulation  of 
which  the  phenomena  of  animal  and  vegetable  life  depend. 

As  heat  penetrates  and  expands  all  bodies,  the  question  natu- 
rally arises,  whether  all  solid  bodies  are  fusible  ?  In  this  respect 
great  differences  present  themselves  amongst  bodies ;  some  are 
easily  fusible,  and  pass  into  a  fluid  condition  at  even  a  low  tem- 
perature, as,  for  instance,  ice,  phosphorus,  sulphur,  wax,  fat,  &c.j 
others,  again,  require  high  temperatures  to  reduce  them  to  fusion, 
as  tin,  lead,  &c. ;  finally,  there  are  bodies  which  only  melt  at  very 


FUSION.  495 

high  temperatures,  as  gold,  iron,  platinum.  No  success  has,  as 
yet,  attended  the  attempts  made  to  fuse  charcoal,  although  many 
natural  philosophers  maintain  that  they  have  observed  traces  of 
fusion  at  the  edges  of  the  diamonds  submitted  to  experiment. 
Judging  from  analogy,  we  must  conclude  that  there  are  no  abso- 
lutely infusible  bodies,  and  that  all  would  melt  if  exposed  to  a 
sufficiently  high  degree  of  temperature. 

Organic  bodies  undergo,  for  the  most  part,  a  chemical  decom- 
position by  the  action  of  heat  before  they  are  reduced  to  a  state 
of  fusion. 

On  a  body  passing  from  the  solid  to  the  fluid  condition,  we  ob- 
serve two  remarkable  phenomena.  In  the  first  place ,  it  remains 
solid  up  to  a  certain  fixed  temperature,  which  is  always  the  same 
for  the  same  body,  and  at  which  alone  fusion  begins ;  and  secondly ', 
the  temperature  does  not  change  during  fusion,  let  the  amount  01 
heat  imparted  be  what  it  may.  Heat  is,  therefore,  absorbed 
during  fusion,  and  incorporates  with  the  body  without  producing 
any  further  action  on  the  feelings  or  on  the  thermometer.  The 
invariability  of  the  fusion  point  and  the  absorption  of  latent  heat 
are  two  essential  conditions  of  fusion. 

The  following  table  gives  the  point  of  fusion  for  different  sub- 
stances. 

Wrought  English  iron  1600  degrees  C.     2912  degrees  F. 

Soft  French  iron  1500       "  2732 

i  The  least  fusible  steel  1400       "  2552 

[The  most  easily  fusible  steel  1300       "  2372 

!:Gray  cast-iron,  second  smelt- 
ing 1200        "  2192 
Easily  fusible  gray  cast-iron  1050        "  1922        " 
Hold                                         1250        "              2302        " 
Silver                                       1000        "              1832 
iironze                                       900        "              1652 
untimony                                  432        "  809        " 
:inc                                           360        "  680 
<ead                                          334        "                633 
fismuth                                     256        "                492 

230        "  448 

talgam,  formed  of  5  parts 
tin,  1  part  lead  194        «  391 


496  LATENT    HEAT. 

Sulphur  109  degrees  C.        228  degrees  F. 
Amalgam  of  8  parts  bismuth, 

5  parts  lead,  3  parts  tin  100  "  212 
Amalgam  of  4  parts  bismuth, 

1  part  lead,  1  part  tin  94  "  200  " 

Sodium  90  "  194  " 

Potassium  58  "  136  " 

Phosphorus  43  "  108  " 

Stearic  acid  70  "  158  " 

Soft  wax  68  "  154  " 

Yellow  wax  61  "  141  " 

Stearine  49  to  43°  120  to  108° 

Spermaceti  49  "  120  " 

Acetic  acid  45  "  113  " 

Soap  33  "  91  " 

Ice  0  "  32  " 

Oil  of  turpentine                     —10  "  —18  " 

Mercury                                   —39  "  —38.2  " 

Latent  Heat. — A  considerable  degree  of  heat  is  necessary  to 
convert  ice  or  snow  at  32°  into  water  at  32°.  The  heat  is  latent 
in  the  water,  and  is  alike  imperceptible  to  the  feelings  or  to  the 
thermometer. 

If  lib.  of  water  of  174°  be  mixed  with  lib.  of  snow  of  32°, 
we  shall  obtain  21bs.  of  water  of  32°.  All  the  heat,  therefore, 
which  was  contained  in  the  hot  water,  is  no  longer  to  be  detected 
by  the  thermometer,  having  alone  been  applied  to  the  purpose  of 
converting  snow  at  32°  into  water  at  32°. 

If  snow,  or  pounded  ice  at  about  — 18°  be  mixed  with  com- 
mon salt  at  about  — 18°,  the  two  will  combine  to  form  a  liquid 
solution  of  salt ;  and  the  thermometer  will,  in  the  mean  time,  fall 
more  and  more,  owing  to  the  large  quantity  of  heat  that  is  latent 
in  the  liquefaction  of  two  previously  solid  bodies.  On  this  prin- 
ciple depend  the  so-called  freezing  mixtures. 

If  we  designate  as  1,  the  amount  of  heat  necessary  to  raise  the 
temperature  of  lib.  of  water  to  1°,  the  amount  of  heat  which 
becomes  combined  or  latent  by  the  fusion  of  lib.  of  snow  will  be 
equal  to  79. 

Heat  is  latent  as  well  in  the  melting  of  ice  and  snow,  as  also 
in  the  fusion  of  other  bodies.  The  following  are  the  values  of 


SOLIDIFICATION.  497 

the  latent  heat  of  several  bodies,  according  to  Irvine's  calcula- 
tions : 

Sulphur  .  .     80 

Lead  .         .         .     90 

Wax  .  .     97 

Zinc  .         .         .274 

Tin  ...  278 

Bismuth  .         .         .  305 

The  signification  of  these  numbers  is  easily  understood ;  for 
instance,  as  lib.  of  snow  requires  for  its  fusion  79  units  of  heat, 
that  is,  79  times  as  much  heat  as  is  necessary  to  raise  the  tempe- 
rature of  lib.  of  water  1°,  80°  units  of  heat  are  requisite  to  fuse 
lib.  of  sulphur,  and  90,  97,  and  274,  respectively,  for  the  fusion 
of  lib.  of  lead,  wax,  or  zinc,  &c. 

As  heat  is  latent  in  the  fusion  of  a  solid  body,  so  likewise  an 
absorption  of  heat  is  effected  on  a  solid  body  being  dissolved 
into  a  fluid  condition;  we  may  easily  convince  ourselves  of  the 
truth  of  this  on  throwing  a  pulverized,  easily  soluble  salt,  as  salt- 
petre, in  water,  and  promoting  the  solution  by  stirring;  the  tem- 
perature of  the  water  will  fall  several  degrees  during  the  process. 

Pulverized  Glauber's  salts,  over  which  muriatic  acid  has  been 
poured,  give  a  fall  of  temperature  of  +  50  to  —  1.4°  F. 

Solidification. — On  the  transition  of  a  body  from  a  fluid  to  a 
solid  condition,  we  observe  phenomena  precisely  analogous  to 
those  exhibited  in  the  process  of  fusion ;  in  the  first  place,  it  only 
occurs  at  a  definite  temperature  corresponding  with  the  fusion 
point ;  and  secondly,  all  the  latent  heat  that  had  been  absorbed  by 
fusion  is  again  liberated  on  solidification  taking  place. 

The  phenomenon  of  the  liberation  of  latent  heat  on  the  solidi- 
fication of  fluid  bodies  was  proved  in  the  following  manner:  In 
the  year  1714  Fahrenheit  made  the  observation,  that  under  cer- 
tain circumstances  pure  water  may  be  cooled  to  from  14°  to  10° 
without  freezing.  This  may  often  be  noticed  in  the  open  air, 
but  the  phenomenon  can  be  best  exhibited  by  being  careful  to 
expose  the  cooling  water  to  but  an  inconsiderable  pressure  of  air 
or  vapor.  This  may  be  effected  by  making  water  boil  in  a  glass 
tube  that  has  been  drawn  out  into  a  fine  point,  and  sealing  it 
when  we  suppose  that  all  the  air  has  been  driven  out  by  the 
steam.  There  will  then  only  be  steam  in  the  glass  above  the 

42* 


498  FORMATION    OF    VAPOR. 

water,  which  will  exercise  but  an  inconsiderable  degree  of  pres- 
sure at  a  low  temperature.  On  exposing  such  a  glass  tube  as  this 
to  a  temperature  of  10°,  the  water  will  remain  fluid;  but  when 
the  vessel  is  shaken,  the  mass  of  water  will  suddenly  freeze.  If 
a  thermometer  has  been  inserted  into  the  interior  of  the  glass 
tube,  on  which  we  may  be  able  to  discern  the  low  degree  of  tem- 
perature, standing  at  10°,  we  shall  see  how  the  mercury  will 
instantaneously  rise  to  32°  as  the  water  becomes  solid. 

The  rapidity  with  which  the  solidification  occurs  under  these 
circumstances,  and  the  rising  of  the  thermometer,  are  phenomena 
which  easily  admit  of  explanation.  The  latent  heat  of  the  first 
particles  that  freeze,  passes  over  to  the  next  particles,  which  are 
still  fluid.  They  are  certainly  warmed,  but  not  sufficiently  so  to 
hinder  their  solidification,  hence  the  twofold  action  of  solidifica- 
tion and  heating. 

When  solidification  takes  place  at  the  ordinary  freezing  point, 
it  always  occurs  but  slowly,  and  without  any  elevation  of  tempe- 
rature. If,  for  instance,  water  freeze  at  32°,  the  solidification 
will  generally  begin  simultaneously  at  various  points,  and  here 
the  particles  first  solidified  will  give  off  their  latent  heat  to  the 
neighboring  parts,  which  will  thus  be  maintained  in  a  fluid  con- 
dition for  a  few  minutes  longer.  This  is  the  cause  of  our  observ- 
ing thin  ice  plates,  and  fine  needles  of  ice  diffusing  themselves  in 
various  ways  over  the  fluid  mass.  In  this  manner  the  latent  heat 
is  distributed  by  degrees,  and  were  it  not  for  the  presence  of  this 
«,  heat,  the  whole  fluid  mass  would,  on  being  cooled  to  the  freezing 
temperature,  at  once  become  solid. 

Heat  is  also  liberated  every  time  a  fluid  enters  into  a  solid 
combination  with  another  body.  Thus,  burnt  gypsum  and  burnt 
lime  combine  with  water  to  form  solid  bodies,  named  hydrates 
by  the  chemists.  Water  passes,  therefore,  by  this  combination 
into  a  solid  form,  and,  consequently,  heat  must  be  liberated.  We 
thus  explain  the  intensity  of  heat  occasioned  by  throwing  water 
on  burnt  lime. 

Formation  of  Vapor. — When  a  fluid  is  in  contact  with  the  air, 
its  quantity  diminishes  by  degrees,  until  it  wholly  disappears  after 
a  longer  or  shorter  period  of  time.  The  water  which  covers  the 
soil  after  rain  cannot  resist  the  action  of  a  dry  wind  or  the  sun- 
shine, but  will  disappear,  not  only  because  it  has  been  imbibed 
by  the  earth,  but  also  because  it  has  evaporated  in  the  air. 


FORMATION    OF    VAPOR. 


499 


The  phenomenon  of  evaporation  goes  on  more  rapidly  on  letting 
water  boil  in  a  flat  dish  over  the  fire ;  in  a  short 
time  all  the  water  will  have  disappeared,  although 
it  has  not  been  absorbed  by  the  dish.  Hence  it 
follows,  that  fluids  change  their  aggregate  condi- 
tion, becoming  invisible  and  expansible  like  gases. 
We  designate  by  the  term  vapor  any  fluid  that 
has  passed  into  a  gaseous  condition. 

The  erroneous  opinion  long  prevailed  that  va- 
pors could  not  exist  by  themselves  as  such  ;  that 
they  were  dissolved  in  the  air  in  the  same  manner 
as  salt  is  in  water;  and,  finally,  that  in  order  to 
make  fluids  assume  the  form  of  gas,  it  was  neces- 
sary to  have  some  solvent  medium  as  the  air,  like 
the  soluble  power  of  water  to  make  salt  fluid.  In 
order  to  prove  the  incorrectness  of  this  view,  and 
at  the  same  time  to  be  able  to  study  the  true  laws 
of  the  formation  of  vapor,  we  must  take  care  to 
conduct  the  process  in  a  vacuum.  For  this  pur- 
pose the  Torricellian  vacuum  is  admirably  well 
adapted,  not  only  from  its  furnishing  us  with  a  perfect  vacuum, 
but,  also,  because  the  depression  of  the  movable  column  of  mer- 
cury affords  us  a  means  of  measuring  the  expansive  force  of 
vapors. 

Let  us  assume  that  we  have  placed  three  Torricellian  tubes  side 
by  side  in  a  broad  vessel  v  v',  Fig.  476,  filled  with  mercury,  the 
fluid  level  will  be  equal  in  all  three ;  if,  however,  by  means  of  a 
curved  pipe  we  pour  a  little  water  into  a  tube  b',  it  will  rise  to  the 
Torricellian  vacuum,  and  the  mercury  will  then  instantly  fall  seve- 
ral millimetres.  This  depression  cannot  be  ascribed  to  the  weight 
of  the  small  layer  of  water  floating  on  the  mercury ;  and,  in  like 
manner,  provided  we  have  taken  water  which  has  been  perfectly 
freed  from  air  by  boiling,  as  is  necessary  to  the  success  of  the 
experiment,  we  are  unable  to  ascribe  this  depression  to  the  air 
liberated  from  the  water.  Vapors  must,  therefore,  have  been  de- 
veloped in  the  water,  which,  like  gases,  possess  a  tension ;  for 
these  vapors  act  precisely  in  the  same  manner  as  if  a  small  por- 
tion of  air  had  been  suffered  to  rise  in  the  vacuum. 

The  amount  of  depression  affords  at  once  a  standard  by  which 
to  measure  the  power  of  tension  in  the  vapor  or  the  steam  of  the 


500 


FORMATION    OF    VAPOR. 


water.  If  we  assume  that  the  surface  of  the  mercury  t,  depressed 
by  the  vapor,  stands  15mm  (0.589  in.)  lower  than  that  c  of  the 
other  barometer,  above  which  there  is  still  a  perfect  vacuum,  it 
will  be  clear  that  the  vapor  will  press  upon  the  surface  t  with  a 
force  equal  to  a  column  of  mercury  15mm  in  height.  This  depres- 
sion of  15mm  is,  therefore,  actually  the  measure  of  the  force  of  ten- 
sion of  the  steam. 

Fig.  477.  ^  we  had  put  sulphuric  ether,  for  instance,  or 
any  other  fluid,  instead  of  water,  into  the  third  baro- 
meter tube  b'f,  we  should  have  observed  a  far  more 
considerable  amount  of  depression  than  in  the  water, 
for,  at  a  medium  temperature,  the  depression  amounts 
to  almost  half  the  height  of  the  barometer  6,  from 
which  it  follows,  that,  under  these  circumstances, 
the  vapor  of  ether  has  a  force  of  tension  equal  to  the 
pressure  of  almost  half  an  atmosphere. 

Maximum  of  the  Force  of  Tension  of  Vapors. — 
The  tendency  of  vapors  to  expand  is  carried,  as  in 
gases,  ad  infinitum;  that  is  to  say,  the  smallest 
quantity  of  vapor  will  diffuse  itself  through  every 
part  of  a  vacant  space,  be  its  size  what  it  may,  ex- 
ercising a  more  or  less  considerable  pressure  upon 
the  walls.  The  smallest  quantity  of  water  is,  there- 
fore, capable,  in  the  form  of  vapor  or  steam,  of  fill- 
ing a  space  of  many  thousand  cubic  metres,  in  the 
same  manner  as  does  the  air.  Although  vapors 
have  an  illimitable  force  of  expansion,  their  force  of 
tension  cannot,  as  in  the  case  of  gases,  be  increased 
at  will  by  an  increase  of  pressure.  For,  to  whatever 
extent  we  compress  a  given  quantity  of  air,  its  elas- 
ticity will,  according  to  Mariettas  law,  increase  in  the  same  pro- 
portion as  its  volume  diminishes.  On  attempting  to  compress 
vapors,  in  order  by  that  means  to  augment  their  elasticity,  we 
soon  reach  a  point  where  the  vapor  condenses,  and  returns  to  its 
fluid  condition.  The  limit  of  resistance,  at  which  further  com- 
pression produces  no  increase  of  elasticity  of  the  vapor,  but  ren- 
ders it  fluid,  is  termed  the  maximum  of  the  tension  of  vapor. 

In  order  to  show,  by  experiment,  this  characteristic  difference 
between  gases  and  vapors,  the  most  efficient  apparatus  is  the  one 
described  at  page  129,  excepting  only  that  ether  is  put  in  the  place 


FORMATION    OF    VAPOR.  501 

of  the  air  in  the  tube  of  the  barometer.  For  this  purpose,  the  Tor- 
ricellian tube  is  carefully  filled  with  mercury,  the  air  being  as 
much  as  possible  removed  by  boiling  or  other  means.  If  the  tube 
be  thus  filled  to  the  height  of  from  1  to  2  centimetres  (0.393  to 
0.786  in.)  with  mercury,  the  remainder  of  the  tube  must  be  filled 
up  with  ether,  on  which  the  tube  is  inverted  and  immersed  in  the 
vessel  c  n.  The  ether  immediately  rises,  one  portion  remaining 
fluid,  while  the  other  is  evaporated  in  the  vacuum,  which  occa- 
sions a  depression  of  the  column  of  mercury.  If,  for  instance, 
the  column  n  s  has  only  a  height  of  400mm  (15.74  in.),  while  it 
would  be  760mm  (30  in.)  in  height  if  there  were  a  vacuum  above, 
then  the  force  of  tension  of  the  vapor  of  ether  is  equal  to  360mm 
(14.19  in.)  If  now  we  press  the  Torricellian  tube  c  cf  more 
deeply  into  the  tube  c  c,  filled  with  mercury,  in  order  thus  to 
diminish  the  space  filled  with  vapor  of  ether,  we  shall  perceive 
that  the  mercury  column  n  s  remains  quite  unchanged.  If  there 
is  air  instead  of  ether  vapor  in  the  upper  part  of  the  tube,  we 
know  that  when  the  volume  of  included  air  is  diminished  by 
being  pressed  down,  its  elasticity  also  increases,  so  that  the 
height  of  the  mercury  column  in  the  barometer  decreases,  (page 
129.)  Here  the  case  is  quite  different  with  regard  to  vapor,  for 
the  volume  of  the  vapor  of  ether  will  be  diminished  without  the 
elasticity  being  increased,  the  height  of  the  column  n  s  remaining 
the  same. 

The  more,  however,  that  we  press  the  tube,  the  more  does  the 
quantity  of  the  ether  increase,  the  diminution  of  the  space  occu- 
pied by  the  ether  vapor  acting  in  such  a  manner  that  a  portion 
of  the  vapor  is  again  condensed  to  fluid  ether,  whilst  the  remain- 
ing vapor  does  not  change  its  force  of  tension.  If,  therefore, 
we  compress  the  space  filled  with  the  ether  vapor  to  J,  J,  or  J, 
&c.,  J,  J,  or  J  &c.  of  the  vapor  will  likewise  be  condensed.  If 
we  continue  to  press  down  the  tube,  we  shall  soon  reach  a  point 
at  which  all  the  vapor  will  be  condensed,  so  that  there  will  be 
only  fluid  ether  over  the  column  of  mercury;  it  is,  however,  ex- 
tremely difficult  fully  to  remove  every  globule  of  vapor,  as  the 
ether  always  contains  absorbed  air. 

On  again  raising  the  tube,  the  column  of  mercury  will  always 
retain  the  same  height  n  s,  whilst  the  fluid  layer  of  ether  will 
continually  diminish ;  showing  that  vapor  re-forms  immediately 
again  to  fill  the  enlarged  space,  and  reaches  the  maximum  of  the 


502  EQUILIBRIUM    OF    THE    FORCE    OF    TENSION. 

power  of  tension.  If,  however,  we  only  put  a  little  ether  into  the 
tube,  and  raise  it  sufficiently  to  let  all  the  fluid  escape,  the  mer- 
cury will  also  ascend  on  continuing  to  raise  the  vessel ;  the  ether 
vapor  is  consequently  no  longer  at  the  maximum  of  the  force  of 
tension,  and  will  exhibit  exactly  the  same  relations  as  a  gas  on  a 
further  increase  of  its  volume. 

Equilibrium  of  the  Force  of  Tension  in  an  Unequally  Heated 
Space. — We  may  easily  convince  ourselves  of  the  important  in- 
fluence exercised  by  the  degree  of  temperature  on  the  maximum 
tension  of  vapors,  by  observing  the  inequality  in  the  depression 
of  the  barometer  tube  during  the  above-named  experiment,  when 
conducted  at  different  temperatures.  For  instance,  with  ether  at 
32°  we  obtain  only  a  depression  of  180mm  (7.08  in.),  whilst  it 
amounts  to  630mm  (24.74  in.)  at  86°.  Phenomena  which  are 
ever  present  before  us  furnish  us  with  many  proofs  of  the  truth  of 
this.  The  vapor  of  water,  as  it  is  formed  upon  the  surface  of 
rivers  and  lakes,  has  only  an  inconsiderable  degree  of  tension; 
but  when  water  is  made  to  boil,  the  force  of  tension  of  the  steam 
is  so  great  as  to  be  able  to  equipoise  the  pressure  of  the  atmo- 
sphere, whilst  at  a  still  higher  temperature  this  tension  augments 
to  such  a  degree,  as  to  occasion  the  most  fearful  explosions  in  the 
boilers. 

We  may  conjecture  from  this  what  the  maximum  of  the  ten- 
sion of  steam  may  be  in  a  space  which  is  unequally  heated  in 
different  parts.  According  to  the  conditions  of  the  equilibrium  of 
gaseous  bodies,  the  steam  must  have  an  equal  degree  of  tension 
at  all  parts  of  this  space ;  and  as  the  force  of  tension  of  the  steam 
cannot  be  so  great  at  the  cooler  as  at  the  warmer  parts,  it  is  evi- 
dent that  the  tension  of  the  vapor  must  be  the 
same  throughout  the  whole  space  as  at  the 
coldest  places ;  that,  consequently,  the  vapor 
cannot  at  the  warmer  parts  reach  the  maxi- 
mum of  the  force  of  tension  corresponding  to 
the  higher  temperature. 

This  principle  may  be  rendered  apparent  by 
the  help  of  the  apparatus  (Fig.  478).  Two  glass 
bulbs,  a  and  6,  each  containing  a  little  ether, 
are  connected  by  a  tube  c,  a  second  curved 
tube  d  passing  through  the  cork  that  closes  b. 
If,  now,  the  ether  in  a  and  b  be  brought  to  the 


ESTIMATE    OF    THE    FORCE    OF    TENSION. 


503 


Fig.  479. 


boiling  point,  (which  is  best  effected  by  plunging  the  tube  into 
hot  water,)  the  vapor  will  escape  through  the  tube  d,  carrying 
away  the  air  from  the  apparatus.  We  now  plunge  the  lower 
end  of  the  tube  d  in  a  vessel  filled  with  mercury,  removing  the 
sources  of  heat  by  which  the  ether  has  been  made  to  boil ;  a  and 
b  will  then  immediately  be  cooled  down  to  the  temperature  of 
the  surrounding  air,  the  force  of  tension  of  the  vapor  in  the  ap- 
paratus will  diminish  to  a  definite  degree,  and  the  mercury  con- 
sequently rise  to  a  definite  height,  dependent  upon  the  temperature 
of  the  surrounding  air.  If  we  plunge  one  bulb  into  snow  or  some 
freezing  mixture,  the  mercury  will  forthwith  rise  as  high  as  if  both 
bulbs  had  experienced  the  same  degree  of  cooling. 

Estimate  of  the  Force  of  Tension  of  the  Vapor  of  Water. — Dif- 
ferent kinds  of  apparatus  have  been  applied  to  the  purpose  of  de- 
termining the  force  of  tension  of  steam,  according  as  we  wish  to 
calculate  it  for  a  temperature  between  32°  F.  and  212°  F.,  below 
32°  or  above  212°. 

The  apparatus  represented  in  Fig.  479,  is  used  for  temperatures 
varying  between  32°  and  212°.     It  consists  of  two  baro- 
meter tubes,  immersed  side  by  side  in  the  same  vessel ; 
the  first  of  these  tubes  forms  a  complete  barometer,  and, 
in  the  second,  there  is,  above  the  mercury,  a  little  water, 
which  forms  a  little  vapor  in  the  vacuum.     The  two 
tubes  are  plunged,  by  means  of  an  iron  rod,  into  a  suffi- 
ciently deep  glass  vessel ;  this  vessel  is  quite  filled  with 
water,  which  may  be  warmed  to  any  tempera-    Fig<480> 
ture  we  please  between  32°  and  212°.     The 
temperature  of  this  water,  which  may  be  deter- 
mined by  properly  applied  thermometers,  is,  at 
the  same  time,  that  of  the  two  barometers,  and 
of  the  steam  in  the  one.     In  order  to  obtain  the 
degree  of  elasticity  of  the  steam  corresponding 
to  each  degree  of  temperature,  we  have  only  to 
determine  in  what  relations  the  depression  of 
the  steam  barometer  stands  to  the  height  of  the 
column  of  mercury  in  the  perfect  barometer. 

The  following  method  may  be  adopted  for 
measuring  the  force  of  tension  of  steam  above 
212°.     A  wider  vessel  is  fixed  into  a  tolerably 
long  glass  tube,  Fig.  480,  somewhat  in  the  same  manner  as  the 
cistern  of  a  barometer;  the  longer  and  shorter  tubes  are  both  open 


504 


ESTIMATE    OF    THE    FORCE    OF    TENSION. 


at  the  top.  On  pouring  in  mercury,  it  will,  of  course,  rise  equally 
high  in  both  tubes.  The  fluid  to  be  tested  is  then  poured  upon  the 
mercury  in  the  wider  tube,  and  after  being  kept  up  to  the  boiling 
point  for  some  time  after  all  the  air  has  been  expelled,  the  tube 
is  sealed.  If  we  put  the  vessel  into  a  fluid,  the  temperature  of 
which  is  above  the  boiling  point  of  the  enclosed  fluid,  vapor  will 
be  formed,  which  presses  upon  the  mercury  (in  the  vessel),  causing 
it  to  rise  in  the  long  tube.  The  difference  of  the  mercury  level 
in  the  vessel  and  the  tube,  indicates  how  much  the  power  of  ten- 
sion of  the  vapor  exceeds  the  amount  of  the  pressure  of  the  atmo- 
sphere. 

The  apparatus  is  fastened  to  a  graduated  stem,  both  for  the 
purpose  of  being  able  to  measure  the  height  to  which  the  column 
of  mercury  is  raised,  and  also  to  protect  the  tube  from  being 
struck  or  broken.  If  the  tube  be  long  enough,  we  may,  by  means 
of  this  apparatus,  measure  the  tension  of  steam  at  3  or  4  atmo- 
spheres. 

In  order  to  be  able  to  measure  higher  tensions,  we  need  only 
fuse  together  the  ascending  tube,  so  that  a  definite  quantity  of 
air  may  be  enclosed  in  it.  When  the  steam  in  the  vessel  drives 
the  mercury  into  the  tube,  the  enclosed  air  becom^l  compressed, 
and  we  may  easily  compute  the  force  of  tension  of  the  steam  by 
the  difference  in  the  height  of  the  two  surfaces  of  mercury. 

The  following  tables  contain  the  maximum  of  the  force  of  ten- 
sion of  steam  for  different  temperatures : 


Degrees. 

Force    of   tension    of 
steam     in     millimetres, 
0.039  inch. 

Pressure  upon  1  square 
centimetre,  0.393  inch  sq., 
in     kilogrammes,     1  5,444 

grs. 

0         32°  F. 

5 

0,007 

10        50     " 

9 

0,013 

20         68     " 

17 

0,023 

30        86     " 

30 

0,042 

40       104     " 

53 

0,072 

50       122     " 

89 

0,126 

60       140     " 

145 

0,196 

70       158     " 

229 

0,311 

80       176     " 

352 

0,478 

90       194     " 

525 

0,714 

100       212     " 

760 

1,033 

OF    THE    VAPOR    OF    WATER. 


505 


Force   of   tension   in 
atmospheres. 

Corresponding  tempe- 
ratures. 

Pressure  upon  1  square 
centimetre,  '393  inch  sq., 
expressed  in  kilogrammes, 

15,444  grs. 

1 

100      212°  F. 

1,03 

2 

121       249     « 

2,07 

4 

145       293     « 

4,83 

6 

160       320     " 

6,20 

8 

172       341     « 

8,26 

10 

182       359     " 

10,33 

15 

200       392     « 

15,49 

20 

215       419     " 

20,66 

25 

226       438     " 

25,82 

30 

236       456     " 

30,99 

We  see  from  these  tables,  that  at  the  temperature  of  the  boiling 
point,  the  force  of  tension  of  steam  equipoises  the  pressure  of  the 
atmosphere.  This  is  universally  true  :  the  force  of  tension  of  the 
vapor  formed  from  any  boiling  liquid  is  always  equal  to  the  pres- 
sure on  the  surface  of  the  liquid ;  for  if  it  were  less,  the  vapor 
could  not  remain  in  the  interior  of  the  liquid  in  the  form  of  bub- 
bles, and  if  it  were  more  considerable  the  vapor  must  have  been 
previously  formed.  The  vapors  of  all  liquids  have  an  equal  force 
of  tension  at  the  boiling  point.  Dalton  was  of  opinion  that  the 
force  of  tension  must  be  equal  at  an  equal  number  of  degrees 
above  or  below  the  boiling  point;  it  would  only  be  necessary, 
therefore,  according  to  this  law,  to  have  a  table  for  the  force  of 
tension  of  saturated  steam,  and  to  know  the  boiling  point  of  a 
liquid,  in  order  to  ascertain  the  force  of  tension  of  the  vapor  at 
any  temperature.  The  boiling  point  of  alcohol,  for  instance,  is 
172°  F.,  the  force  of  tension  of  the  vapor  of  alcohol  at  235°,  that 
is,  63°  above  the  boiling  point,  must  be  equal  to  the  force  of  ten- 
sion of  steam  at  275°,  which  is  2280mm  (89.76  in.)  or  3  atmo- 
spheres. According  to  this  law,  the  force  of  tension  of  the 
saturated  vapor  of  alcohol  at  32°  would  be  equal  to  19mra  (-748 
in.),  because  this  is  the  force  of  tension  of  steam  at  a  temperature 
172°  F.  below  the  boiling  point  of  water.  From  the  experiments 
of  many  natural  philosophers  it  is  evident,  however,  that  this  law 
is  not  correct. 

The  force  of  tension  of  vapor  increases,  as  we  see,  in  a  far  more 
rapid  ratio  than  the  temperature;  that  is  to  say,  a  definite  eleva- 
43 


506  OF    THE    VAPOR    OF    WATER. 

tion  of  temperature  produces  a  far  greater  increase  of  the  force  of 
tension  at  high  than  at  low  degrees  of  temperature.  Thus,  while 
an  elevation  of  temperature  from  212°  to  249°  (that  is,  about  37°) 
increases  the  force  of  tension  of  steam  about  1  atmosphere;  it 
will  increase  at  an  elevation  from  438°  to  456°  (that  is,  at  only 
18°  more)  about  5  atmospheres,  consequently  between  438°  and 
456°,  an  elevation  of  temperature  of  only  3f  °  would  suffice  to 
raise  the  force  of  tension  of  steam  to  about  1  atmosphere. 

There  are  two  reasons  for  the  increase  of  the  force  of  tension  at 
an  increasing  temperature.  Let  us  suppose  some  enclosed  space 
to  be  filled  by  steam  at  212°,  that  is,  with  a  vapor  whose  force  of 
tension  equals  1  atmosphere,  and  that  there  is  no  more  water  in 
this  space,  it  being  entirely  precluded  from  ingress.  If,  now,  the 
temperature  of  this  space  be  raised  to  249°,  the  vapor  will  strive 
to  expand,  and  since  it  will  not  be  able  to  do  so,  its  force  of  ten- 
sion will  increase,  although  not  much ;  the  vapor  will  then  be  no 
longer  saturated,  but  quite  in  the  condition  of  a  gas.  If,  how- 
ever, there  still  remain  any  water  in  this  space,  then,  in  conse- 
quence of  the  increase  of  temperature,  a  new  quantity  of  vapor 
will  be  formed  of  1  atmosphere;  if,  then,  the  force  of  tension 
increases  by  1  atmosphere,  the  vapor  will  become  denser,  when, 
in  consequence  of  its  greater  density,  it  will  exercise  a  greater 
pressure. 

1  cubic  inch  of  water  yields: 

1700  cubic  inches  of  saturated  steam  at  212° 
897          "  "  "    249 

207          "  "  "    359 

There  are  liquids  whose  boiling  points  lie  below  the  average 
temperature  of  the  air,  and  such  bodies  can  of  course  not  become 
liquid  under  ordinary  circumstances,  being  at  the  usual  tempe- 
rature, and  the  usual  pressure  of  the  atmosphere,  in  a  gaseous 
form,  such  gases  must,  therefore,  be  compressed  and  cooled,  in 
order  to  become  liquid.  Thus,  for  instance,  we  find  sulphurous 
acid  at  14°,  and  when  rendered  liquid  under  pressure  in  a  glass 
tube,  its  vapors  exert  a  pressure  of  about  5  atmospheres,  even 
at  77°. 

Cyanogen  gas,  ammonia,  carbonic  acid,  &c.,  also  admit  of 
being  condensed  into  liquids  by  compression  and  cooling.  The 
vapor  of  liquid  carbonic  acid  has  at  32°  a  force  of  tension  of  36, 
and  at  86°  a  force  of  tension  equal  to  73  atmospheres. 


THE    STEAM    ENGINE. 


507 


The  Steam  Engine. — Steam  has,  in  more  recent  times,  as  we 
all  know,  been  used  as  a  moving  force,  and  it  is  owing  to  the 
introduction  of  the  steam  engine  that  industry  and  general  inter- 
course among  men  have  made  such  rapid  advances.  Passing  by 
the  older  forms  of  this  machine,  we  will  at  once  enter  upon  the 
consideration  of  Watts'  steam  engine.  The  cylinder  JJ  is  made 
air-tight  below  as  well  as  above,  so  that  the  atmospheric  air 
cannot  pass  on  either  side  upon  the  piston  C.  The  steam  which 
is  conducted  from  the  boiler  through  the  tube  Z  of  the  engine, 
enters  the  cylinder  alternately  at  E  and  D.  We  shall  presently 
enter  fully  into  the  manner  in  which  this  alternation  is  produced. 
In  the  position  of  the  engine,  as  seen  in  our  figure,  the  steam 
enters  above  at  E.  The  steam  in  the  lower  part  of  the  cylinder 
escapes  at  D,  in  order  to  reach  the  condenser  T  through  the  pipe 
H,  and  is  there  condensed ;  the  steam  presses  above  upon  the 
piston  C,  while  below  it  there  is  a  rarefied  space ;  the  piston, 
therefore,  is  in  the  act  of  descending. 

Fig.  481. 


508  THE   STEAM   ENGINE. 

The  condensation  of  the  steam  in  the  cylinder  on  the  one  side 
of  the  piston  takes  place  by  the  latter  being  brought  into  con- 
nection with  the  above-mentioned  condenser;  this  is  the  space 
marked  /,  being  connected  either  with  the  lower  or  the  upper 
part  of  the  cylinder.  Cold  water  is  constantly  poured  into  the 
condenser,  and  a  condensation  of  the  steam  thus  effected ;  but  by 
this  means,  in  accordance  with  the  principles  illustrated  by  Fig. 
472  (page  502),  the  force  of  tension  of  the  steam  is  diminished  in 
that  part  of  the  cylinder  which  is  connected  with  the  condenser; 
the  steam  then  passes  from  the  cylinder  into  the  condenser,  to  be 
there  condensed. 

Many  contrivances  have  been  proposed  for  making  the  steam 
enter  the  cylinder  alternately  from  above  and  below,  whilst  the 
steam  escapes  from  the  other  side  of  the  piston  towards  the  con- 
denser. The  simplest  of  these  arrangements  is  the  cross-cock. 
This  is  perforated,  as  seen  in  Fig.  482.  The  tube  .K"  leads  to  the 
boiler,  C  to  the  condenser,  0  to  the  upper,  and  U  to  the  lower 
part  of  the  cylinder.  If  the  cross-cock  be  placed  in  the  position 

Fig.  482.  Fig.  483.  aS   S6en   In  FiS'  482>   the    Steam 

will  flow  from  the  boiler  into  the 
upper  part  of  the  cylinder,  whilst 
its  under  part  is  connected  by  the 
tubes  U  and  C,  with  the  con- 
denser. When  the  piston  has 
penetrated  far  into  the  cylinder, 
the  cross-cock  is  brought,  by  a  half  revolution,  into  the  position 
seen  in  Fig.  483.  Now  the  tubes  K  and  U  are  connected,  the 
steam,  therefore,  enters,  escaping  from  the  upper  part  of  the 
cylinder  through  the  tubes  0  and  C  towards  the  condenser; 
now,  therefore,  there  must  be  an  upward  directed  motion  of  the 
piston. 

The  cross-cock  has  not  proved  to  be  applicable  to  larger  en- 
gines, owing  to  the  impossibility  of  making  the  channels  of  the 
cock  wide  enough  to  admit  of  the  passage  of  the  requisite  quantity 
of  steam.  The  sliding  valve  is  now  most  generally  made  use  of, 
it  is  applied  to  the  engine  we  have  delineated,  and  is  represented 
in  Figs.  484  and  485,  in  its  two  extreme  positions,  being  drawn 
on  a  large  scale.  The  steam  passes  through  the  tube  Z  to  a  re- 
ceiver, from  which  the  tubes  D  and  E  lead  to  the  cylinder.  This 
receiver  is  divided  into  two  separate  spaces  by  means  of  the  slide 


THE   STEAM   ENGINE. 


509 


Fig.  484. 


Fig.  485. 


F.  The  middle  portion  m  of  the  receiver  is  quite  shut  off  from 
the  upper  part  a',  and  the  lower  part  a,  whilst  these  two  spaces 
are  themselves  connected  by  the 
cavity  of  the  slide.  The  steam 
now  flows  from  the  boiler  into  the 
space  m,  the  spaces  a  and  a  re- 
maining connected  with  the  con- 
denser. If  the  sliding  valve  have 
the  position  of  Fig.  484,  the  steam 
will  flow  from  m  through  the  com- 
munication E  from  above,  into  the 
cylinder ;  while  the  steam  passes 
under  the  piston,  through  that  of 
D  to  a,  and  from  thence  to  the 
condenser.  If,  however,  the  slid- 
ing valve  lie  in  the  position  repre- 
sented in  Fig.  485,  the  steam  will 
flow  from  m  through  D  from  be- 
low into  the  cylinder,  the  steam 
above  the  piston  will  pass  through 
E  towards  af,  and  from  thence 
through  the  sliding  valve  to  a,  and 
finally  reach  the  condenser. 

The  sliding  valve  has  been  re- 
presented in  Fig.  486,  as  seen  in 
.the  direction  of  Z,  in  order  that 
we  may  form  to  ourselves  a  per- 
fectly correct  idea  of  its  construc- 
tion. The  manner  in  which  the 
slide  is  drawn  up  and  down  the 
machine,  will  presently  be  further 
considered. 

The  condenser  T,  Fig.  481, 
stands  in  a  receiver  partly  filled 
with  cold  water,  constantly  flow- 
ing into  the  condenser  from  an 
opening  not  visible  in  our  figure. 
The  quantity  of  the  water  enter- 
ing may  be  increased  or  dimin- 
ished at  will,  by  means  of  a  cock. 

43* 


Fig.  486. 


510  THE   STEAM   ENGINE. 

The  water  is  pumped  out  of  the  condenser  by  the  pump  K.  As 
is  well  known,  more  or  less  air  is  always  absorbed  in  all  water ; 
this  is  liberated  in  the  boiler,  and  passes,  together  with  the  steam, 
through  the  engine  into  the  condenser.  In  the  same  manner,  air 
will  be  disengaged  from  the  cold  water  flowing  into  the  condenser. 
The  steam  will  become  condensed,  while  the  air  will  remain  in  a 
gaseous  condition.  This  air  would,  by  degrees,  accumulate  in 
the  condenser,  and  thus  prevent  the  creation  of  a  vacuum  on  the 
one  side  of  the  piston,  if  it  were  not  at  the  same  time  carried  off 
by  the  pump  K,  which  has,  on  that  account,  received  the  name 
of  an  air-pump. 

By  means  of  this  pump,  the  water  is  carried  from  the  condenser 
into  the  receiver  jR,  from  which  it  is  almost  entirely  discharged  by 
the  tube  S.  The  heat  which  was  latent  by  the  evaporation  of 
the  water  in  the  boiler,  is  again  liberated  by  the  condensation  of 
the  steam  in  the  condenser;  this  liberated  heat  raises  the  tempera- 
ture of  the  cold  water  thrown  into  the  condenser;  the  water  carried 
through  the  pump  K  towards  R  is  therefore  warm,  on  which  ac- 
count it  is  more  advantageous  than  cold  water  for  feeding  the  boiler. 
The  water  required  for  the  boiler  passes  through  the  tube  Mto  a 
pump,  which  carries  it  through  the  tube  M f.  This  pump,  as  well 
as  the  air-pump,  is  put  into  motion  by  the  engine  itself;  for  in- 
stance, the  pump  rod  L  is  attached  to  the  beam,  and  is  raised  as 
the  piston  C  descends,  and  is  pressed  down  as  the  latter  ascends. 
When  the  piston  of  the  warm  water  pump,  attached  to  the  rod  L, 
rises,  the  suction  valve  v  opens,  and,  at  the  descent  of  the  piston, 
the  valve  n. 

On  the  other  side  of  the  beam,  exactly  behind  L,  there  is 
another  pump  rod,  through  which  cold  water  is  raised  into  the 
tube  Tf,  and  brought  through  U  into  the  receiver  containing  the 
condenser. 

Let  us  now  consider  how  the  upward  and  downward  motion  of 
the  piston  C  is  transmitted. 

The  piston  rod  moves,  air  and  steam  tight,  through  the  stuffing- 
box  in  the  middle  of  the  upper  cover  of  the  cylinders ;  being  con- 
nected with  the  end  of  the  beam  by  a  system  of  movable  rods, 
bearing  the  name  of  the  parallelogram.  The  object  of  this  con- 
trivance is  merely  to  establish  a  perfectly  vertical  motion  of  the 
piston  rod,  which  could  not  be  effected  if  the  rod,  or  handle,  were 
fastened  directly  to  the  end  of  the  balancer;  since  it  would,  in 


THE   STEAM   ENGINE.  51 1 

that  case,  deviate  alternately  to  the  left  and  right,  and,  conse- 
quently, so  much  affect  the  stuffing-box,  that  the  air-tightness 
would  soon  be  destroyed. 

The  one  end  of  the  working  beam  is  alternately  drawn  up  and 
down  by  the  piston,  while  its  other  extremity  has  constantly  an 
opposite  motion:  that  is  to  say,  when  the  piston  Crises, the  right 
arm  of  the  beam  goes  down,  and  vice  versa.  The  upward  and 
downward  motion  of  the  beam  is  constantly  changed  into  a  cir- 
cular motion  by  the  connecting  rod  P,  and  the  crooked  handle  Q. 
The  axis  of  this  handle  is  the  main  axis  of  the  machine  which 
is  to  be  set  in  motion,  and  around  this  axis  moves  the  fly- 
wheel X. 

The  motion  of  the  piston  Cis  very  irregular.  As  it  comes  to  a 
state  of  rest  at  the  upper  and  lower  end  of  the  cylinder,  and  then 
reverses  its  motion,  it  is  evident  that  it  cannot  perform  its  course 
with  uniform  velocity.  Its  velocity  is  greatest  when  it  passes  the 
middle  of  the  cylinder,  and  diminishes  the  more  it  approaches 
either  end.  On  considering  the  motion  of  the  handle,  we  shall 
find  that,  with  uniform  velocity  of  revolution,  the  motion  in  a  ver- 
tical direction  is  still  very  changeable.  The  handle  stands  in  a 
horizontal  position  when  the  piston  C  is  in  the  middle  of  the 
cylinder,  at  which  moment  the  motion  of  the  handle  is  in  a  ver- 
tical direction ;  this  motion  inclines,  however,  horizontally  when 
the  piston  C  attains  its  highest  or  lowest  position.  The  vertical 
portion  of  the  motion  of  the  handle  is  perfectly  similar  to  the 
motion  of  the  piston ;  in  proportion  as  the  motion  of  the  handle 
becomes  more  horizontal,  the  velocity  of  the  piston  diminishes, 
without  any  diminution  in  the  velocity  of  the  revolving  action  of 
the  handle. 

The  diameter  of  the  path  traversed  by  the  handle  Q,  is  of 
course  equal  to  the  height  of  the  cylinder,  allowing  for  the  thick- 
ness of  the  piston,  provided  that  both  arms  of  the  beam  are  of 
equal  length ;  the  length  of  the  arm  of  the  handle  Q  is,  therefore, 
equal  to  half  the  length  to  which  the  piston  can  be  raised. 

The  fly-wheel  X  serves  to  maintain  uniformity  in  the  motion  of 
the  engine.  Even  if  the  pressure  of  the  steam  upon  the  piston 
were  quite  invariable,  it  could  not  equally  contribute  to  the  revo- 
lution of  the  handle  in  all  its  positions.  Indeed,  we  may  consider 
the  pressure  acting  by  means  of  the  connecting  rod  P  upon  the 
handle,  as  divided  into  forces  at  right  angles  to  each  other,  the 


512  THE    STEAM    ENGINE. 

one  acting  in  the  direction  of  the  handle  itself,  as  pressure  upon 
the  axis  does  not  contribute  to  produce  revolution ;  this  is  brought 
about  entirely  by  the  force  acting  tangentially  to  the  curve  of  the 
handle.  The  amount  of  these  forces  varies  at  every  moment. 
When  the  arm  of  the  handle  stands  vertically,  every  pressure  pro- 
ceeding from  the  piston  acts  solely  and  alone  as  pressure  upon 
the  axis  of  the  curved  handle.  If  the  engine  were  to  be  brought 
to  a  stand-still  in  this  position,  the  greatest  pressure  applied  to  the 
piston  would  be  unable  to  set  it  in  motion;  the  only  reason,  there- 
fore, that  the  engine  does  not  remain  absolutely  motionless  on 
coming  into  this  position  is,  that  the  individual  parts  of  the  engine 
continue  their  motion  by  virtue  of  the  inertia,  in  the  same  manner 
as  a  pendulum  moves  on  by  virtue  of  its  inertia  when  arrived  at 
its  position  of  rest.  When  once  the  curved  handle  has  passed  its 
vertical  position,  that  portion  of  the  pressure  transmitted  by  P, 
and  which  occasioned  the  revolution  of  the  handle,  is  increased 
more  and  more,  and  attains  its  maximum  when  the  arm  of  the 
handle  is  directed  horizontally.  The  force,  therefore,  which 
turns  the  handle,  varies  constantly,  becoming  null  twice  during 
one  complete  revolution,  both  when  the  arm  of  the  handle  attains 
its  highest  and  its  lowest  position ;  and,  in  like  manner,  it  twice 
attains  a  maximum.  If  we  examine  the  motion  produced  by  so 
variable  a  force,  we  shall  easily  see  that  it  can  only  be  alternately 
accelerated  and  retarded.  If  the  circle  represented  in  Fig.  487 
exhibit  the  path  described  by  the  handle,  we  shall  perceive  that 
an  acceleration  of  motion  will  take  place  from  b 
to  d,  because  here  the  moving  force  will  act  with 
the  greatest  energy.  The  motion  accumulated, 
as  it  were,  in  the  parts  of  the  machine  must,  how- 
ever, diminish  as  the  arm  of  the  handle  moves 
from  d  to  /*,  because  the  moving  force  has,  in  the 
mean  time,  become  very  weak,  and  even  abso- 
lutely null,  and  thus  a  retardation  is  caused  of  motion  by  these 
hinderances ;  on  the  way  from  f  to  h  it  is  again  accelerated,  and 
again  retarded  from  h  to  b. 

These  alternations  in  the  motion  of  the  curved  handle  lie  in  the 
nature  of  things,  and  cannot  be  wholly  avoided.  The  differences 
between  the  greatest  and  the  least  velocity  become,  however, 
smaller  in  proportion  to  the  magnitude  of  the  inert  mass  to  be 
moved ;  by  means  of  a  sufficiently  large  balance  wheel,  we  may 


THE    STEAM    ENGINE.  513 

render  these  differences  in  the  velocity  of  revolution  so  inconside- 
rably small,  as  to  exercise  no  further  injurious  influence.  The 
force  acting  on  the  part  from  6  to  d,  and  more  strongly  from/  to 
h,  cannot  effect  any  marked  increase  of  velocity,  as  it  must  move 
a  very  considerable  inert  mass;  as,  however,  a  considerable 
quantity  of  motion  is  accumulated  in  the  balance  wheel,  the  de- 
crease in  the  quantity  of  motion,  as  the  handle  passes  from  d  to/, 
or  from  b  to  h,  is  not  sufficiently  great  to  occasion  a  perceptible 
diminution  of  velocity. 

The  balance  wheel  thus  equalizes  the  irregularity  of  motion 
inherent  in  the  arrangement  of  the  engine.  The  work  which  a 
steam  engine  may  have  to  perform,  be  it  of  what  kind  it  may, 
never  opposes  an  absolutely  uniform  resistance  to  the  moving 
force ;  and  this  would  occasion  irregularity  in  the  working  of  the 
whole  engine,  were  it  not  otherwise  rendered  uniform  by  the 
balance-wheel. 

As  the  work  to  be  performed  by  the  engine,  that  is,  the  resistance 
to  be  overcome,  increases  or  diminishes,  the  going  of  the  engine 
will  become  quicker  or  slower.  Momentary  disturbances  of  this 
kind  will  be  equalized  by  the  balance  wheel,  while  a  universal 
diminution  of  the  resistance  and  the  load  would  be  followed,  pro- 
vided the  afflux  of  steam  remained  the  same,  by  a  continually  in- 
creasing acceleration  in  the  motion  of  the  engine.  In  order  that 
the  velocity  may  not  exceed  certain  limits,  a  valve  must  be 
attached  to  the  steam  pipe,  in  order  that  the  ingress  of  steam  may 
be  more  or  less  retarded,  according  as  the  valve  passes  more  and 
more  from  the  horizontal  position  (that  of  perfect  aperture),  to  the 
vertical  (that  of  perfect  closure).  The  turning  of  this  valve  must, 
however,  be  effected  by  the  engine  itself,  and  this  is  done  by 
means  of  an  apparatus  termed  the  regulator. 

A  somewhat  tense  string  i  passes  round  the  rotating  axis  of  the 
balance  wheel  over  a  vertical  wheel  o,  Fig.  488,  in  such  a  man- 
ner that  the  wheel  o  is  made  to  rotate  by  the  revolution  of  the 
principal  axis.  A  vertical  conical  wheel  is  fastened  to  the  axis  of 
the  disc  o,  whose  teeth  work  into  a  similar  wheel  placed  horizon- 
tally, and  which  is  thus  made  to  rotate  on  its  vertical  axis.  This 
axis  is  prolonged  into  a  rod,  to  the  upper  end  of  which  the  coni- 
cal pendulum  Fis  attached. 

The  pendulum  V  consists  of  two  heavy  balls  so  fastened  to  the 
upper  end  of  the  vertical  rod  that  by  its  rapid  rotation,  the  balls 


514 


THE    STEAM    ENGINE. 

Fig.  488. 


fly  apart,  owing  to  their  centrifugal  force.  The  rods  to  which  the 
balls  are  attached,  are  connected  by  means  of  a  nut  h  surrounding 
the  vertical  rod.  The  nut  h  is  raised  up  as  soon  as  the  balls  fly 
apart;  and  by  this  motion  of  h  the  angular  lever  r  s  a  is  turned 
round  Jhe  axis  s,  the  rod  a  b  drawn  towards  the  right  side,  by 
which  the  angular  lever  b  c  d  is  turned  round  the  axis  c,  and  the 
rod  e  d  thus  finally  drawn  down ;  but  as  e  is  the  extreme  point  of 
a  lever  arm,  the  rotating  axis  of  which  is  the  axis  round  which  the 
valve  moves  in  the  tube  Z,  the  valve  is  closed  by  this  point  e 
being  drawn  down.  The  whole  lever  system  of  which  we  have 
been  speaking  here  is  only  represented  in  outline  in  our  Figure, 
it  being  placed  on  the  front  side  of  the  engine,  and,  therefore, 
really  not  visible  from  the  point  of  view  in  our  sectional  delinea- 
tion of  the  engine. 

The  working  of  the  cross-cock,  or  the  raising  and  lowering  of 
the  sliding  valve,  in  short,  the  motion  of  the  apparatus  which 


THE   STEAM   ENGINE. 


515 


serves  to  conduct  the  steam  alternately  to  the  upper  and  lower 
part  of  the  cylinder  must  be  effected  by  the  engine  itself.  The 
instrument  by  which  this  motion  is  produced,  is  designated  the 
governor. 

The  most  important  external  portion  of  the  governor,  is  the 
eccentric  disc,  indicated  in  our  Fig.  488  by  the  letter  y.  This  is  a 
circular  metallic  plate  fastened  to  the  axis  of  the  fly-wheel,  whose 
central  point  does  not,  however,  correspond  with  the  central  point 
of  revolution,  as  may  be  more  plainly  seen  in  Fig.  489.  During 

Fig.  489. 


every  revolution  of  the  axis  the  central  point  of  the  eccentric  disc 
describes  a  circle.  A  ring  passes  around  the  circumference  of 
the  eccentric  disc,  prolonged  towards  the  one  side  into  a  rod, 
whose  end  fits  at  Tinto  a  lever  arm  revolving  round  a  fixed  axis  F. 
The  distance  of  the  centre  of  the  eccentric  disc  from  T  varies,  as 
the  lever  arm  F  T  passes,  and  returns  to  the  position  seen  in 
Fig.  490,  during  each  entire  revolution  of  the  main  axis ;  the 

Fig.  490. 


chord  of  the  one  described  in  this  manner  by  the  point  T  is,  how- 
ever, evidently  equal  to  the  diameter  of  the  circle  described  by 
the  central  point  of  the  eccentric  disc. 

The  axis  of  jP  passes  through  the  whole  width  of  the  machine, 


516 


THE    STEAM    ENGINE. 


Fig.  491. 


as  may  be  plainly  seen  in  Fig.  491,  where  this  axis  is  represented 

at  its  full  length.  To  this  axis  are 
attached  two  perfectly  equal  and 
parallel  lever  arms  N9  on  either  side 
of  the  receiver,  in  which  the  sliding 
valve  is  enclosed.  Fig.  489  exhi- 
bits only  one  of  these  in  its  true 
form,  while  both  are  seen  fore- 
shortened in  Fig.  491.  To  each  of 
these  lever  arms  a  vertical  bar  M, 
directed  upwards,  is  secured,  being 
connected  at  the  top  by  a  horizontal 
transverse  bar  Q,  supporting  in  its 
centre  the  bar  R,  to  which  the  slid- 
ing valve  is  attached.  This  rod 
passes,  air  and  steam-tight,  through 
a  stuffing-box  into  the  receiver  of 
the  sliding  valve.  The  motion  of 
the  lever  JV*  produces,  by  means  of 
the  rods  M,  an  alternate  raising 
and  lowering  of  the  transverse  rod 
Q,  by  which  the  sliding  valve  is  also  raised  up  and  down. 

Let  us  now  consider  the  influence  exercised  by  the  removal  of 
the  condenser.  If  the  steam  act  on  the  one  side  of  the  piston 
with  a  force  of  tension  of  one  atmosphere,  while  the  part  of  the 
cylinder  lying  on  the  other  side  is  in  connection  with  the  air,  and 
not  with  the  condenser,  the  pressure  of  the  steam  on  the  one  side 
of  the  piston  will  be  equal  to  the  pressure  of  the  atmospheric  air 
on  the  other  side,  and,  consequently,  there  can  be  no  motion.  In 
order  to  produce  this,  it  is  necessary  to  raise  the  force  of  tension 
of  the  steam.  Provided  this  have  been  made  equal  to  the  pres- 
sure of  two  atmospheres,  the  effect  will  be  precisely  the  same  as 
if  there  were  a  vacuum  on  the  one  side  of  the  piston,  while  the 
steam  pressed  upon  the  other  side  with  the  force  of  tension  of  one 
atmosphere ;  the  half  of  the  effective  power  of  the  steam  being 
thus  lost  in  overcoming  the  resistance  of  the  air.  If  the  moving 
steam  had  actually  a  force  of  tension  equal  to  3,  4,  5,  &c.,  atmo- 
spheres, ^,  J,  or  i,  &c.  of  this  power  would  be  lost  in  overcoming 
the  resistance  of  the  air  if  there  were  no  condenser.  The  greater, 


THE    STEAM   ENGINE.  517 

therefore,  the  force  of  tension  of  the  steam  acting  in  the  engine, 
the  less  will  be  the  loss  of  power  in  overcoming  atmospheric 
resistance  where  there  is  no  condenser.  If,  therefore,  the  steam 
that  is  to  move  the  engine,  has  only  a  force  of  tension  equal  to 
one  atmosphere,  or  but  a  little  more,  a  condenser  will  be  indis- 
pensably necessary;  if,  however,  the  force  of  tension  of  the  effect- 
ive steam  be  greater,  the  engine  may  act  without  a  condenser, 
the  advantage  of  which  will  diminish  in  proportion  to  the  increase 
in  the  force  of  tension  of  the  moving  steam.  The  resistance 
which  has  to  be  overcome  in  the  moving  of  the  condensing  pump 
(air-pump),  exhausts,  however,  also  a  portion  of  the  power  of  the 
steam.  Thus,  at  a  certain  amount  of  steam  pressure,  the  advan- 
tages afforded  by  the  condenser  are  again  counteracted  by  the 
resistance  of  the  air-pump ;  and,  consequently,  in  this  case  it  is 
quite  immaterial  whether  or  not  we  use  a  condenser.  In  engines, 
worked  by  steam,  of  still  stronger  force  of  tension,  the  condenser 
is  more  disadvantageous  than  the  contrary,  and  in  such  apparatus 
it  is,  therefore,  wholly  omitted. 

Such  steam  engines  as  are  worked  with  a  condenser  are  called 
low  pressure  engines,  while  those  that  have  no  condensers  are 
termed  high  pressure  engines. 

High  pressure  engines  are  more  simple  in  their  construction 
than  those  of  low  pressure,  owing  to  the  absence  of  a  condenser 
and  air-pump,  and  the  former  may  be  used  of  much  smaller 
dimensions  than  the  latter,  and  yet  produce  the  same  result;  for 
the  combined  pressure  of  steam  having  a  force  of  tension  equal  to 
4  atmospheres  acting  upon  a  surface  of  1  square  foot,  is  as  great 
as  the  combined  pressure  of  steam  with  a  force  of  tension  equal  to 

atmosphere  acting  upon  a  surface  of  4  square  feet.  From  these 
causes,  high  pressure  engines  are  used  wherever  it  is  desirable  to 
use  an  engine  of  considerable  force  in  a  small  compass. 

[As  the  steam  engine,  invented  by  Oliver  Evans,  of  Philadel- 
phia, in  1784,  and  patented  by  the  State  of  Maryland  in  1787,  may 
be  considered  as  the  origin  of  all  the  high  pressure  engines  now 
in  use,  however  modified,  the  following  description  and  repre- 
sentation of  it,  Fig.  492,  as  given  by  Prof.  Johnson,  (Scientific 
Class  Book,  319,)  are  worthy  of  attention. 

A.  Working  cylinder,  to  which  the  steam,  equal  to  several  at- 
mospheres in  pressure,  is  admitted  by  the  pipe  o,  and  the  rotary 
valve  v. 
44 


518 


THE    STEAM    ENGINE. 


S.  Smoke  pipe  arising  from  the  inferior  flue,  after  the  latter 
leaves  the  head  of  the  boiler. 

G.  Fire  grate,  or  furnace,  from  which  the  flame  passes  in  the 
direction  marked  by  the  arrow. 

P.  Force  pump,  which  draws  the  water  from  the  reservoir  of 
hot  water  R,  situated  above  it.  This  water  is  kept  hot  by  the 
steam  escaping  from  the  cylinder  A,  after  it  has  fulfilled  its  duty 
there. 


THE    LOCOMOTIVE. 


519 


520  THE    LOCOMOTIVE. 

p.  Pump  rod  connected  with  the  beam  above.  V.  Safety  valve 
connected  with  the  boiler,  and  furnished  with  a  graduated  lever 
and  weight,  to  regulate  the  pressure. 

/.  Working  beam  connected  to  an  upright  support  by  rods 
k  k,  to  oscillating  triangle  T",  to  pump  rod  p,  piston  rod  /,  and  to 
shackle  bar  6,  which  last  gives  motion  to  fly-wheel  W. 

g  is  a  toothed  wheel,  geared  to  another  of  the  same  diameter, 
which,  being  connected  with  the  two  equal  bevel  wheels  at  e, 
communicate  motion  to  the  rotary  valve  v. 

s  is  the  escape  pipe,  by  which  the  steam  is  conducted  to  the 
tank  or  reservoir  jR.] 

One  of  the  best  known  and  most  interesting  high  pressure  en- 
gines is  the  Locomotive  used  on  railroads.  See  Fig.  493.  A 
is  the  furnace :  the  fuel  is  thrown  upon  the  grate  through  the 
opening  a,  which  may  be  closed  by  a  door.  There  is  no  escape 
for  the  heated  air  from  the  furnace,  excepting  through  a  series  of 
horizontal  tubes,  leading  from  Jl  to  D ;  from  D  the  heated  air 
passes  with  the  smoke  out  at  the  chimney.  In  Fig.  494  we  see 
how  these  tubes  lie  above  and  beside  each  other.  These  tubes  are 
carried  through  a  space  filled  with  water,  besides  which  the  fur- 
nace itself  is  enclosed  on  all  sides  by  water.  From  the  extraor- 
dinarily large  surface  with  which  the  water  is  in  this  manner 
brought  into  contact,  a  considerable  quantity  of  steam  is  formed 
at  every  moment.  The  steam  is  collected  over  the  water  in  the 
space  marked  B  and  C ;  and  from  C  it  is  carried  through  the  tube 
c  to  the  cylinder.  If  the  mouth  of  the  tube  c  were  situated  very 
low  down,  a  large  quantity  of  water  would,  by  the  violent  boiling, 
be  mechanically  carried  into  the  tube  c,  and  from  thence  into  the 
cylinder.  To  prevent  this,  the  steam  chamber  at  C  is  elevated. 
The  tube  c  soon  branches  ofFinto  two  tubes  d  and  df,  as  may  be 
plainly  seen  in  Fig.  496.  In  Fig.  495  there  is  only  one  of  these 
tubes  visible,  viz.  d.  Each  leads  to  a  receiver  i,  from  which  the 
steam  enters  the  cylinder  F.  On  either  side  lies  a  cylinder,  as 
seen  in  Fig.  496  ;  Fig.  495  exhibits  only  one,  viz.,  the  front  one 
of  these  cylinders.  It  is  represented  lengthwise  here ;  the  surface 
of  the' section  does  not,  however,  correspond  with  the  whole  of  the 
remaining  figure,  but  lies  in  front  of  it.  The  cylinders  lie  hori- 
zontally, and  the  piston,  together  with  the  piston  rods,  passes 
backwards  and  forwards  in  a  horizontal  position.  Two  passages 
run  to  either  end  of  the  cylinder  from  the  receiver  i,  to  which  the 


THE    LOCOMOTIVE. 


521 


44' 


522  THE    LOCOMOTIVE. 

steam  is  conducted  by  the  tubes  c  and  d.  On  the  lower  side  of 
the  receiver  i,  a  slide  moves  backwards  and  forwards,  and  forms 
at  the  middle  a  box  o  which  opens  downwards.  The  position  indi- 
cated in  Fig.  493  shows  both  passages  closed  by  means  of  this 
slide.  If  we  suppose  this  to  be  so  far  moved  to  the  left,  that  the 
passage  to  the  left,  instead  of  being  closed,  opens  into  the  cavity 
o,  that  to  the  right  will  be  brought  into  connection  with  the  steam 
reservoir  i ;  in  this  position  of  the  slide  the  steam  will  enter  on  the 
right  side  into  the  cylinder  F,  and,  consequently,  drive  the  piston 
to  the  left,  whilst  the  steam  will  pass  from  the  left  side  of  the 
piston,  through  the  passage  to  the  left,  into  the  box  o,  and  from 
thence  to  the  chimney  through  the  tubes  p  and  q.  If,  however, 
the  slide  were  pushed  to  the  fullest  extreme  towards  the  right, 
the  steam  would  flow  from  i  through  the  passage  to  the  left  into 
the  cylinder,  escaping  on  the  other  side  to  the  right  through  the 
passage  into  the  box. 

The  piston  rod  is  secured  by  so-called  connecting  rods,  that  is, 
it  is  prevented  by  this  means  from  deviating  from  its  course,  and 
is  thus  only  able  to  pass  to  and  fro  in  the  same  straight  line.  To 
the  piston  rod  is  immediately  attached  the  driving  rod,  which 
turns  the  crank  n  round  its  axis  m.  The  middle  wheels  of  the 
engine  are  also  fastened  to  the  axis  m,  so  that  by  each  movement 
of  the  piston,  a  complete  revolution  of  the  wheel  is  effected;  thus, 
at  every  forward  and  backward  movement  of  the  piston,  the  engine 
is  propelled  a  distance  equal  to  the  circumference  of  the  middle 
wheels. 

To  this  axis  m  is  likewise  attached  the  eccentric  disc,  by  which 
the  slide  in  the  receiver  i  is  moved.  As  may  be  seen  in  our 
Figure,  the  x  shaped  extremity  of  the  rod,  fastened  to  the  ring  of 
the  eccentric  disc,  grasps  the  upper  part  of  the  lever,  whose  ful- 
crum is  at  s.  By  the  motion  of  this  lever,  the  bars  t  fastened  to 
it  are  moved  to  and  fro,  and  with  them  the  slide. 

By  the  raising  of  the  lever  JV,  the  X  shaped  extremity  of  the 
bar  is  pressed  down,  and  a  retrograde  motion  thus  imparted  to 
the  locomotive ;  but  here  we  must  end  our  description,  as  we  are 
unable  to  pursue  it  in  detail,  .ff  and  L  are  safety  valves;  /  is  the 
steam  whistle. 

[The  locomotive  engines  constructed  in  this  country  differ  some- 
what from  the  foregoing  in  their  details,  and,  therefore,  the  repre- 
sentation of  Fig.  497,  one  of  Baldwin's  excellent  locomotives,  has 


THE    LOCOMOTIVE. 


523 


524  THE    LOCOMOTIVE. 

been  given  for  the  purposes  of  comparison  ;  and  it  will  be  per- 
ceived that  it  is  far  more  powerful  and  efficient  than  those  figured 
and  described  by  the  author.] 

The  effect  which  a  steam  engine  is  capable  of  producing,  that 
is,  the  power  of  the  machine,  depends  upon  the  quantity  of  water 
which  in  a  given  time  can  be  converted  into  steam  in  the  boiler; 
let  us,  therefore,  examine  into  the  action  which  a  litre  of  water 
can  produce  when  converted  into  steam.  If  we  assume  that  the 
surface  of  the  piston  is  1  square  decimetre  (3.93  inches  sq.), 
and  the  height  of  the  cylinder  (the  height  to  which  the  piston  can 
be  raised)  is  10  decimetres  (1  yd.  3  inches),  the  contents  of  the 
cylinder  will  be  10  cubic  decimetres,  or  10  litres  (610.28  cubic 
inches);  in  order,  therefore,  to  drive  the  piston  to  the  top,  10  litres 
of  steam  must  pass  from  the  boiler  into  the  cylinder.  If,  now, 
the  steam  has  a  force  of  tension  equal  to  1  atmosphere,  the  pres- 
sure exercised  upon  every  square  centimetre  (.393  inch  sq.)  of 
the  surface  of  the  piston  is  about  1  kilogramme  (2J  Ibs.  tr.),  and 
the  combined  pressure  upon  the  whole  piston,  consequently,  100 
kilogrammes  (250  Ibs.  tr.) ;  if,  therefore,  there  existed  no  impedi- 
ments to  motion,  we  might  load  the  piston  with  100  kilogrammes 
(250  Ibs.  tr.),  and  this  weight  would  be  lifted  10  decimetres  (1 
yd.  3  in.),  if  we  conducted  10  litres  (21.13  pts.)  of  steam  at  212° 
into  the  cylinder.  The  effect,  therefore,  that  can  be  produced  by 
10  litres  (21.13  pts.)  of  steam  at  212°,  is  capable  of  raising  100 
kilogrammes  (250  Ibs.  tr.)  to  the  height  of  10  decimetres  (39.37 
in.),  or  of  raising  1000  kilogrammes  (2500  Ibs.  tr.)  to  a  height  of 
1  decimetre  (3.93  in.).  A  litre  (2.11  pts.)  of  water  yields,  how- 
ever, 1700  litres  (3587  pts.)  of  steam  at  212°;  with  1  litre  of 
water,  therefore,  when  converted  into  steam,  we  may  produce  an 
effect  capable  of  raising  170,000  kilogrammes  (425,000  Ibs.  tr.) 
to  the  height  of  1  decimetre  (3.93  in.). 

In  order  the  better  to  calculate  the  power  of  an  engine,  it  is 
usual  to  compare  them  with  horse  power.  If  we  assume  that  one 
horse  is  able  to  raise  750  kilogrammes  (1875  Ibs.  tr.)to  the  height 
of  1  decimetre  (3.93  in.)  in  one  second  of  time,  (the  best  obser- 
vations on  the  labor  of  horses,  and  the  profitable  application  of 
their  powers,  yield  a  result  equivalent  to  the  above  named,)  we 
should  say,  that  an  engine,  in  which  sufficient  steam  was  formed 
every  second  to  raise  750  kilogrammes  (1875  Ibs.)  to  the  height 


THE    LOCOMOTIVE.  525 

of  1  decimetre  (3.93  in.),  (or  534  Ibs.  to  the  height  of  1  foot,)  was 
a  one-horse  power  engine. 

But  the  steam  obtained  from  1  litre  of  water  will  be  capable  of 
raising  170,000  kilogrammes  (425,000  Ibs.)  to  the  height  of  1 
decimetre  (3.93  in.);  if,  therefore,  1  litre  (2.11  pts.)  of  water 

be  converted  into  steam  in  the  boiler  in  17Q'000  /425,000\ 

750     \    1875   /' 

sequently  in  226  seconds,  the  total  effect  which  the  steam  in  this 
engine  can  produce,  is  equal  to  one-horse  power.  A  machine  of 
this  kind  consumes,  therefore,  about  15  litres  (31.70  pts.)  of  water 
in  an  hour. 

All  the  mechanical  power  of  steam  cannot,  however,  be  reckoned 
as  available.  Much  is  lost  owing  to  the  piston  not  acting  in  an 
absolute  vacuum,  to  the  friction  of  the  piston  to  be  overcome,  and 
the  number  of  pumps  that  must  be  set  in  motion,  &c.  All  these 
resistances  diminish  the  available  effect  of  the  machine  to  almost 
the  half  of  the  calculated  power. 

Great  advantage  has  been  obtained  in  the  high-pressure  engines 
by  the  application  of  the  expansion  of  the  steam  in  the  cylinder, 
which  is  effected  by  cutting  off  the  afflux  of  steam  from  the 
boiler  into  the  cylinder,  when  the  piston  has  traversed  J  or  f , 
&c.,  of  its  course.  That  a  greater  effect  can  be  produced  with 
an  equal  expenditure  of  steam  by  the  application  of  the  principle 
of  expansion,  may  be  perceived  by  the  following  simple  conside- 
rations. 

If,  during  the  whole  time  in  which  the  piston  is  rising,  steam 
pours  into  the  steam  cylinder,  (as  is  generally  the  case  in  ordi- 
nary engines,)  having  a  power  of  tension  which  we  will  assume 
to  be  equal  to  2  atmospheres,  the  whole  cylinder,  when  the  piston 
is  quite  raised,  will  be  filled  with  steam  having  a  power  of  ten- 
sion equal  to  2  atmospheres;  and  during  the  time  the  piston  is 
being  raised,  there  will  be  a  mechanical  effect  produced,  which 
we  will  designate  as  E. 

If  now  we  suffer  steam  of  double  the  force  of  tension,  that  is, 
equal  to  4  atmospheres,  to  enter  the  cylinder,  the  pressure  against 
the  piston  will  be  twice  as  great,  and  the  mechanical  effect  E  will 
be  produced  when  the  piston  is  only  half  raised ;  that  is,  when  it 
reaches  the  middle  of  the  cylinder.  If,  at  this  moment,  the 
further  afflux  of  steam  to  the  cylinder  be  prevented,  the  piston 
will  continue  the  rest  of  its  course,  whilst  the  pressure  acting  upon 


526  THE    LOCOMOTIVE. 

it  will  diminish  by  degrees  to  the  half;  and  when  it  reaches  the 
end  of  its  course,  the  force  of  tension  of  the  steam  will  still  be 
equal  to  2  atmospheres. 

Since,  during  the  first  half  of  the  ascent  of  the  piston,  the 
mechanical  effect  E  is  already  produced,  then  the  whole  effect 
which  the  steam  produces  during  the  second  half  of  the  piston's 
ascent  while  so  expanding,  that  its  tension  diminishes  from  4  to 
2  atmospheres,  may  be  considered  as  gain ;  for  the  quantity  of 
steam  filling  the  cylinder  at  the  close  of  the  piston's  motion,  is 
precisely  as  large  as  if  steam,  having  a  force  of  tension  of  2 
atmospheres,  had  flowed  in  while  the  piston  was  completing  its 
motion. 

The  steam  is  generally  cut  off  by  means  of  a  special  expansion- 
slide.  In  ordinary  machines,  the  steam  flows  from  the  boiler 
directly  into  the  chamber,  in  which  the  sliding  valves  move,  to 
admit  of  the  entrance  of  the  steam,  first  to  the  one  and  then  to  the 
other  side  of  the  piston ;  we  will  call  this  chamber  a. 

In  expansion  engines,  there  is  usually,  in  front  of  this,  another 
chamber,  b ;  in  the  plate  between  b  and  a  there  is  an  opening, 
through  which  the  steam  passes  from  b  to  a;  this  opening  can 
be  closed  at  the  proper  times  by  a  second  slide  at  b.  The  motion 
of  this  expansion-slide  is  effected  by  a  properly  placed  eccentric 
disc  in  the  same  manner  as  the  motion  of  the  sliding  valves. 

The  conversion  of  fluids  into  gaseous  bodies  is  commonly  termed 
evaporation.  Liquids  can  either  be  evaporated  by  boiling,  when 
vapors  are  formed  throughout  the  whole  mass,  or  by  exhalation, 
when  the  formation  of  vapor  is  limited  to  the  surface  of  the 
liquid. 

On  observing  the  boiling  of  a  liquid,  we  generally  see  a  more 
or  less  energetic  motion  pervading  all  the  particles;  but,  if  the 
liquid  be  boiled  in  a  glass  vessel,  we  may  observe  bubbles  of 
steam  formed  at  the  warmer  sides  of  the  vessel  and  rise  to  the 
top.  Although  at  first  small,  they  soon  increase  in  volume  as 
they  rise.  The  bubbles  succeed  each  other  most  rapidly  at  the 
hottest  parts  of  the  side.  In  order  that  bubbles  may  be  formed 
in  the  liquid,  which  exercises  a  pressure  upon  them  from  all 
sides,  the  steam  expanding  them  must  have  a  force  of  tension 
equal  to  the  pressure  surrounding  them.  The  first  condition  of 
boiling  is,  therefore,  that  the  temperature  be  sufficiently  high  to 


THE    LOCOMOTIVE.  527 

enable  the  force  of  tension  of  the  steam  to  sustain  the  pressure 
acting  from  all  sides  upon  the  bubbles  of  steam.  A  second  con- 
dition is,  that  sufficient  heat  be  present  to  be  absorbed  as  latent 
heat  during  the  formation  of  steam. 

From  the.  first  condition,  it  follows  that  the  boiling  point  of  a 
liquid  varies  with  the  pressure  on  it ;  and,  from  the  second,  that 
the  rapidity  of  boiling  depends  on  the  amount  of  heat  which  can 
be  conveyed,  in  a  given  time,  through  the  sides  of  the  vessel  to  the 
liquid. 

At  the  level  of  the  sea,  and  at  the  mean  pressure  of  30  inches, 
pure  water  boils  at  212°;  on  the  summit  of  Mont  Blanc,  at  an 
elevation  of  4775  metres,  (15,518  ft.,)  where  the  pressure  of  the 
atmosphere  amounts  only  to  417mm,  water  boils  at  a  temperature 
at  which  the  force  of  tension  of  steam  is  417ram  (16.41  in.) ;  that 
is,  at  about  183°.  At  still  greater  elevations,  water  would  boil 
at  lower  temperatures.  If  we  have  a  table  of  the  force  of  tension 
of  the  vapor  of  a  liquid,  we  may  easily  find  the  temperature  of  the 
boiling  point  at  a  given  pressure ;  for  it  is  the  same  degree  of 
temperature  at  which  the  force  of  tension  of  the  saturated  vapor 
is  equal  to  that  pressure.  We  may,  conversely,  bring  a  liquid  at 
any  given  temperature  to  the  boiling  point,  by  sufficiently  dimi- 
nishing the  pressure. 

At  a  pressure  of  30mm,  (1.18  in.,)  for  instance,  the  boiling  tem- 
perature of  water  is  86°,  because,  at  this  temperature,  the  force  of 
tension  of  the  saturated  steam  is  30mm  (1.18  in.).  Under  a  pres- 
sure of  10mm  (.393  in.),  water  boils  at  51°,  and  under  a  pressure 
of  5ram  (.196  in.),  at  32°. 

The  truth  of  these  data  may  be  shown  by  experiment.  Water 
at  86°  must  be  put  in  a  glass  vessel  under  the  exhausted  receiver 
of  the  air-pump:  after  a  few  strokes  of  the  piston,  the  barometer 
gauge  will  show  a  pressure  only  of  30mm  (1.18  in.),  and  the  boil- 
ing will  then  begin  with  the  same  energy  as  if  the  water  stood  in 
the  open  air  over  a  hot  fire.  This  boiling,  however,  will  soon 
cease,  because  the  receiver  will  be  filled  with  steam,  which  will 
press  upon  the  liquid;  another  stroke  of  the  piston  will  soon 
remove  this  steam,  and  cause  the  boiling  to  recommence.  It  is 
not  possible  in  our  air-pumps  to  make  water  boil  at  32°,  as  no 
rarefaction  of  5mm  (.196  in.)  can  be  produced,  owing  to  the  con- 
tinual re-formation  of  steam  on  the  surface  of  the  water. 


528 


THE    LOCOMOTIVE. 


In  the  apparatus  seen  in  Fig.  498,  we  observe  an  analogous, 
but  still  more  striking  phenomenon.  A  balloon 
with  a  long  neck  a  is  half  filled  with  water  ;  when, 
by  the  boiling  of  the  liquid,  all  the  air  has  been 
driven  out,  the  neck  is  closed  by  a  cork,  and  the 
balloon  inverted,  as  seen  in  Fig.  498.  When  left 
to  itself,  we  perceive  no  ebullition,  but  as  soon  as 
cold  water  is  poured  upon  the  part,  the  water  begins 
to  boil  with  energy.  This  is  owing  to  the  steam 
being  condensed  in  the  upper  part  of  the  balloon, 
and  the  pressure  on  the  liquid  being  thus  dimi- 
nished. 

The  variations  in  the  boiling  point  have  been 
confirmed  by  direct  experiments,  made  at  elevated  districts  in  the 
Alps,  the  Pyrenees,  and  other  mountain  ranges. 

Boiling  water  is,  consequently,  not  equally  hot  at  all  places  on 
the  earth,  and,  therefore,  not  everywhere  alike  applicable  to  do- 
mestic purposes,  and  the  preparation  of  food.  At  Quito,  for 
instance,  water  boils  at  194°,  and  this  temperature  is  too  low  for 
boiling  many  substances  which  require  a  temperature  of  212°. 

As  the  barometer  constantly  varies  at  one  and  the  same  place, 
it  follows  that  the  boiling  point  varies  also. 

If  we  increase  the  pressure  on  fluids,  we  find  that  their  ebulli- 
tion is  retarded,  and  we  may  even  prevent  this  entirely  if  we 
make  the  pressure  sufficiently  strong.  This  is  the  case  with  the 
apparatus  known  by  the  name  of  Papin's  Digestor,  see  Fig.  499. 
By  means  of  this,  water  may  be  heated  to  a  very 
high  temperature  without  boiling.  The  appara- 
tus consists  of  a  cylindrical  vessel  of  iron,  or,  still 
better,  of  brass  or  copper,  the  sides  of  which  are 
capable  of  sustaining  a  very  considerable  degree 
of  pressure.  The  opening  is  provided  with  a 
safety-valve,  which  can  be  closed  and  loaded,  so 
that  it  shall  require  a  pressure  of  from  40  to  50 
atmospheres  to  raise  it.  Boiling  is  rendered  im- 
possible, as  the  steam,  which  is  above  the  liquid, 
is  unable  to  escape,  and,  consequently,  exercises  a  sufficiently 
strong  pressure  to  prevent  it.  As  soon  as  the  valve  is  opened, 
the  steam  issues  with  great  force;  the  temperature  of  the  vessel 
falls,  however,  simultaneously,  as  all  the  heat  which  had  been 


Fig.  499. 


THE    LOCOMOTIVE.  529 

combined  is  given  off  at  once  by  the  energetic  formation  of 
steam. 

This  digester  was  invented  in  the  middle  of  the  17th  century 
by  Papin,  a  learned  man,  residing  at  Marburg  and  Cassel.  It 
served  for  a  number  of  remarkable  experiments,  partly  to  prove 
the  mechanical  force  of  steam,  and  partly  to  show  the  solvent 
force  of  water  when  heated  above  212°.  People  learnt  with 
astonishment,  that  as  nutritious  a  substance  might  be  drawn  from 
bones  as  from  the  most  juicy  portions  of  the  muscle. 

On  causing  water  to  boil  in  a  vessel  from  which  the  steam  can 
only  escape  through  a  proportionately  small  opening,  we  observe 
an  elevation  of  the  boiling  point.  All  the  steam  that  has  been 
formed  by  the  heat  passing  every  moment  into  the  liquid,  can  only 
escape  through  a  small  opening,  if  a  greater  rapidity  of  motion 
has  been  imparted  by  the  greater  force  of  tension  of  the  steam. 

Not  only  the  steam  pressing  upon  the  surface  of  a  liquid  mass, 
but  likewise  the  weight  of  the  column  of  liquid  acts  upon  the  par- 
ticles in  the  interior.     If,  for  instance,  we  had  a  boiler  filled  to  a 
height  of  32  feet  with  water,  a  pressure  of  2  atmospheres  would 
act  upon  the  bottom,  and  here,  consequently,  steam-bubbles  would 
be  formed  at  a  temperature  of  250°.     But  as  the  temperature  of 
the  liquid  mass  on  the  surface  cannot  rise  above  212°,  the  liquid 
will  constantly  ascend  from  the  bottom,  owing  to  its  less  specific 
weight.    As  the  pressure  decreases  with  the  ascent,  steam-bubbles 
are  formed ;  but  their  temperature  decreases,  however,  from  250° 
to  212°.     These  bubbles,  which  are  formed  at  the  bottom  of  the 
vessel,  increase  in  size  as  they  rise,  owing  to  the  pressure  acting 
upon  them  becoming  continually  less.     These  phenomena  may 
be  observed  even  in  small  vessels,  in  which  the  water  only 
mounts  to  a  few  inches  in  depth.     Before  perfect  ebullition  has 
een  established,  bubbles  of  steam  are  formed  at  the  bottom ; 
hich,  however,  are  condensed  on  their  ascending,  owing  to  their 
ntering  layers  of  water  whose  temperature  is  too  low.     Hence 
rises  the  peculiar  sound  which  we  perceive  some  minutes  before 
erfect  boiling  has  commenced.     On  making  the  experiment  in 
glass  bulb,  we  may  observe  how  bubbles  are  formed  at  the 
ottora,  how  they  ascend,  and  then  disappear;  and  we  then  say 
le  water  sings.     This  singing  is  a  sign  that  the  water  will  soon 
e  in  a  state  of  perfect  ebullition. 
45 


530  EVAPORATION—LATENT    HEAT    OF    VAPORS. 

Boiling  is  likewise  retarded  by  substances  which  are  dissolved 
in  the  water ;  thus,  a  saturated  solution  of  common  salt  brine  boils 
at  227°,  a  solution  of  saltpetre  at  240°,  a  saturated  solution  of 
acetate  of  potass  at  336°,  of  nitrate  of  ammonia  at  356°. 

Evaporation  is  the  term  applied  to  the  formation  of  vapor  on 
the  free  surface  of  a  liquid ;  whilst,  as  we  have  seen,  ebullition 
consists  in  vapor  being  formed  in  the  interior  of  the  liquid  mass. 
Water  evaporates  from  the  surface  of  rivers,  lakes,  and  seas,  and 
the  surface  of  damp  ground  and  plants.  The  vapor  has  here, 
evidently,  too  inconsiderable  a  force  of  tension  to  overcome  the 
pressure  of  the  atmospheric  air.  Daily  observation  shows  us  that 
vapor  is  formed  at  every  degree  of  temperature,  and  that  it  dis- 
tributes itself  through  the  air  even  at  the  weakest  degree  of  ten- 
sion. It  was  formerly  assumed  that  a  chemical  affinity  existing 
between  the  molecules  of  the  air  and  those  of  vapor  was  the 
cause  of  this  phenomenon ;  we  have  seen,  however,  that  there  is 
no  need  of  having  recourse  here  to  chemical  forces.  The  steam 
of  water,  be  its  force  of  tension  ever  so  inconsiderable,  mixes 
with  the  air  the  same  as  two  gases  mix.  The  only  condition  ne- 
cessary, therefore,  for  the  evaporation  of  a  liquid  is,  that  the  sur- 
rounding layers  of  air  be  not  saturated  with  vapor;  as,  further, 
in  the  mixture  of  two  gases,  the  molecules  of  the  one  form  a  me- 
chanical impediment  to  the  distribution  of  those  of  the  other,  the 
air  acts  as  a  hinderance  in  evaporation  to  the  rapid  dispersion  of 
the  vapor.  In  a  perfectly  calm  atmosphere,  therefore,  evaporation 
goes  on  very  slowly,  whilst  it  progresses  rapidly  in  an  agitated 
state  of  air;  the  liquid  then  comes  continually  into  contact  with 
new  layers  of  air,  that  are  not  saturated  with  vapor.  Hence  it 
happens  that  water  evaporates  very  quickly  when  a  dry  wind  is 
in  rapid  motion. 

Latent  Heat  of  Vapors. — When  a  liquid  evaporates,  it  must 
absorb  heat ;  this  absorbed  heat  is  as  imperceptible  to  the  feelings 
and  the  thermometer  as  the  heat  which  becomes  latent  by  fusion. 
That  heat  is  latent  in  the  formation  of  vapor,  is  proved  by 
the  temperature  of  the  liquid  remaining  unchanged  during  ebulli- 
tion.' The  temperature  of  boiling  water  remains  at  212°,  how- 
ever much  we  may  increase  the  fire;  all  the  heat  which  is  added 
to  the  boiling  water  serves  only  to  convert  water  at  212°  into 
steam  at  212°. 


LATENT    HEAT    OF    VAPORS. 


531 


Fig.  500. 


The  absorption  of  heat  during  the  evaporation  of  liquids  may 
easily  be  rendered  perceptible  to  the  feelings.  On  pouring  but  a 
few  drops  of  an  easily  evaporable  liquid,  as  spirits  of  wine,  sul- 
phuric ether,  &c.,  upon  the  hand,  we  experience  a  sensation  of 
cold  because  the  hand  has  been  deprived  of  the  heat  drawn  away 
for  the  evaporation  of  the  liquid.  If  we  surround  the  bulb  of  a 
thermometer  with  cotton  wool,  and  then  moisten  the  latter  with 
sulphuric  ether,  the  thermometer  will  fall  several  degrees. 

After  having  learnt  to  know  the  manner  in  which  heat  becomes 
latent  in  the  formation  of  vapor,  it  remains  to  determine  the 
amount  of  this  heat ;  that  is,  to  ascertain  how  much  heat  is 
necessary  to  convert  a  definite  quantity  of  a  liquid  into  vapor. 

Fig.  500  represents  a  glass  bulb  a, 
in  which  water  is  kept  boiling  by 
means  of  a  spirit  lamp ;  if,  now,  the 
vapor  formed  be  conducted  through 
a  glass  tube  b  into  a  cylindrical  vessel 
c  filled  with  cold  water,  the  vapor 
here  will  be  condensed,  and  conse- 
quently, the  heat  which  was  ab- 
sorbed at  a,  in  the  formation  of  vapor, 
will  be  again  liberated  at  c;  the  cold 
water  at  c  will  be  thus  gradually 
jwarmed,  and  from  the  elevation  of  temperature  thus  produced, 
|we  may  determine  the  amount  of  the  latent  heat  of  vapors. 

If  we  assume  that,  after  ebullition  has  been  going  on  for  some 
e  in  the  vessel  a,  all  the  air  has  been  wholly  expelled,  and  the 
of  a  crooked  tube  be  then  plunged  into  the  cold  water  of  the 

•linder  c,  all  the  bubbles  of  vapor  will  at  once  be  condensed  as 

;y  come  into  contact  with  the  cold  water.     In  proportion,  how- 

•er,  as  the  water  becomes  warmer  in  c,  the  bubbles  will  likewise 
.e  larger,  until  finally,  even  if  the  water  at  c  be  heated  to 

,e  boiling  point,  the  bubbles  will  rise  uncondensed  through  the 
>le  mass  of  liquid,  and  a  state  of  ebullition  be  established  at  c. 
.t  the  moment  in  which  ebullition  begins  at  c,  the  experiment 
be  interrupted  by  our  removing  the  glass  cylinder  c. 

Provided  now,  that  there  had  been  11  cubic  inches  of  water  at 
at  the  beginning  of  the  experiment,  the  cylinder  at  the  close 

the  experiment  would  have  contained  13  cubic  inches  of  water 


532  LATENT    HEAT    OF    VAPORS. 

at  212°,  2  cubic  inches  of  water  having  been  thus  added.  This 
additional  water  has  now  been  evaporated  in  the  vessel  a,  and 
again  condensed  in  the  cylinder  c ;  the  latent  heat,  which  was  com- 
bined in  a  has  become  liberated  in  c,  and  has  heated  the  11  cubic 
inches  of  water  from  32°  to  212°;  the  same  amount  of  heat, 

therefore,  which  has  been  absorbed 
by  the  evaporation  of  2  cubic  inches 
of  water,  was  sufficient  to  raise  the 
temperature  of  the  11  cubic  inches  of 
water  from  32°  to  212°.  But  now 
2  are  to  11  as  1  to  5,5,  and  we  may 
therefore  express  the  result  of  our 
experiment  in  the  following  manner : 
The  amount  of  heat  necessary  to  con- 
vert a  definite  quantity  of  water  from 
212°  into  steam  at  212°,  suffices  to 
raise  the  temperature  of  a  mass  of  water  5|  times  greater,  from 
32°  to  212°. 

We  have  already  stated,  that,  for  the  unit  of  heat,  that  quantity 
of  heat  is  assumed,  which  is  requisite  to  raise  the  temperature  of 
1  Ib.  of  water  1°;  to  raise  the  temperature  of  5J  Ibs.  of  water  to 
the  same  amount,  5,5  are  therefore  necessary,  and  550  such  units 
of  heat  to  raise  the  temperature  of  this  mass  212°. 

The  latent  heat  of  1  Ib.  of  steam  is  consequently  equal  to  550. 
The  above  given  experiment  is  not  calculated  to  determine  the 
latent  heat  of  steam,  affording  always  more  or  less  incorrect  re- 
sults. It  is,  however,  well  adapted  to  show  the  connection  of 
the  matter.  The  reason  of  the  special  want  of  accuracy  attend- 
ing the  results  of  this  experiment,  is,  that  at  the  high  temperature 
to  which  water  must  be  raised  in  the  cylinder  c,  a  considerable 
loss  of  heat  is  experienced  by  all  that  surrounds  it ;  a  not  incon- 
siderable amount  of  steam  is  condensed  in  the  tube,  giving  off  to 
the  air  heat  that  is  set  free,  and  which  comes  to  the  cylinder  c 
as  water.  We  may,  therefore,  easily  understand,  that  until  the 
water  in  c  is  made  to  boil,  more  water  will  pass  over  from  the 
vessel  a  than  would  be  the  case  if  these  two  sources  of  error  were 
not  present ;  hence  this  experiment  is  of  little  value  in  giving  the 
latent  heat  of  steam.  We  cannot  here  enter  more  fully  into  the 
consideration  of  the  more  precise  methods  in  use  for  ascertaining 
this  amount. 


LATENT    HEAT    OF    VAPORS.  533 

In  distillation,  the  vapors  formed  in  any  vessel  by  heat  are  con- 
ducted into  a  pipe  surrounded  by  cold  water,  and  the  vapor  is 
converted  into  a  liquid  state  ;  the  temperature  of  the  cold  water 
is,  however,  considerably  raised  in  the  heat  liberated  by  the  con- 
densation of  the  vapor.  This  may  be  easily  shown  by  means  of 
a  small  still,  (Fig.  502,)  in  which  the  vapor  is  conducted  from  the 
glass  bulb  in  which  it  is  formed,  into  a  straight  tube,  passing 
through  a  wider  one,  which  contains  the  cold  water.  The  cold 

Fig.  502.  Fig.  503. 


water,  which  enters  the  condensing  tube,  flows  forth  from  the  other 
end  heated.  In  distillations  conducted  on  a  large  scale,  the  tube 
in  which  the  vapor  is  condensed  has  the  form  of  a  helix,  and  is 
conducted  through  the  vessel  filled  with  the  cold  water,  as  seen 
in  Fig.  503,  in  order  that  the  vapor  may  remain  as  long  as  pos- 
sible in  contact  with  the  cold  water,  and  that  we  may  be  quite 
sure  that  no  vapor  will  escape  from  the  open  end  of  the  tube  in 
an  uncondensed  state.  When  an  apparatus  of  this  kind  has  been 
in  operation  for  some  time,  we  shall  always  find  the  upper  layers 
of  the  water  in  the  refrigerator  very  hot,  owing  to  the  heated  water 
constantly  rising  to  the  surface. 

We  might  determine  the  value  of  the  latent  heat  of  vapors  by 
any  distillatory  apparatus,  if  it  were  possible  every  time  accu- 
rately to  calculate  the  amount  of  vapor  condensed  in  a  given 
time,  and  the  quantity  of  heat  yielded  by  it  to  the  cold  water ; 
in  order,  therefore,  accurately  to  determine  the  latent  heat  of 
vapors,  it  is  only  necessary  to  construct  an  apparatus  in  such  a 

45* 


534  FREEZING    OF    WATER    IN    A   VACUUM. 

manner  as  to  enable  us  to  obtain  these  amounts  with  exactitude. 
According  to  this  principle,  the  latent  heat  of  the  vapors  of  dif- 
ferent liquids  has  been  ascertained.  Thus — 

The  latent  heat  of  steam  is  .     540 

"         "         vapor  of  alcohol      .     214 
"         "         sulphuric  ether        .       90 

That  is  to  say,  in  order  to  convert  1  Ib.  of  these  liquids  into 
vapor  under  the  pressure  of  one  atmosphere,  540, 214,  or  90  times 
as  much  heat  is  combined  as  is  necessary  to  raise  the  temperature 
1  Ib.  of  water  1°. 

The  latent  heat  of  vapors  is  not  the  same  for  all  temperatures, 
being  greater  for  low,  and  less  for  high  temperatures. 

Production  of  Cold  by  Evaporation. — If  a  liquid  boil  in  the  open 
air,  it  will  retain  a  constant  temperature,  owing  to  its  constantly 
receiving  as  much  heat  through  the  sides  of  the  vessel  as  is  ab- 
sorbed by  the  formation  of  vapor.  But  when  ebullition  goes  on 
under  the  air-pump,  the  temperature  continually  falls,  because  the 
vapor  withdraws  from  the  fluid  itself,  and  from  the  surrounding 
bodies,  the  latent  heat  necessary  to  its  formation.  The  following 
experiments  may  be  explained  by  the  absorption  of  heat  which 
takes  place  in  rapid  evaporation. 

Freezing  of  Water  in  a  Vacuum. — We  place  under  the  receiver 
of  the  air-pump  a  broad  glass  dish  filled  with  sulphuric  acid.  A 
few  inches  above  it  is  a  thin  flat  metallic  capsule,  as  seen  in  Fig. 
504,  containing  a  small  quantity  of  water.  This  capsule  is  gene- 
rally suspended  by  three  threads,  or  is  made 
to  rest  upon  three  fine  metallic  feet,  which 
stand  upon  the  edge  of  the  lower  glass  ves- 
sel. A  few  minutes  after  the  air  has  been 
as  much  as  possible  exhausted,  we  see  ice 
needles  upon  the  capsule,  and,  after  a  time, 
the  whole  mass  becomes  solid.  This  remark- 
able experiment  was  first  made  by  Leslie. 
The  sulphuric  acid  absorbs  the  steam  as  soon  as  it  is  formed,  and 
thus  maintains  a  rapid  evaporation.  All  bodies  that  absorb  steam 
with  energy  produce  the  same  action.  The  metallic  capsule  ought 
to  be  extremely  thin,  in  order,  likewise,  to  take  part  in  the  cool- 
ing, and  must  be  insulated  from  the  surrounding  part  by  means 


FREEZING   OF   MERCURY.  535 

of  bad  conductors,  so  that  none  of  the  external  heat  may  be  con- 
veyed to  the  water. 

In  Wollastorfs  Kryophorus  water  likewise  freezes  by  its  own 
evaporization.     Two  glass  bulbs,  Fig.  505,  are  connected  by  a 
tube.     A  little  water  is 
poured  into  each  bulb,  e 

and  by  its  boiling,  all  the 
air  is  driven  from  the 
apparatus.  When  this  is 
done,  the  aperture  at  e  is  fused  by  the  blow-pipe,  and  the  whole 
thus  rendered  air-tight.  If,  now,  all  the  water  be  suffered  to  flow 
into  one  bulb,  while  the  other  is  plunged  into  a  freezing  mixture, 
the  condensation  of  the  steam  constantly  going  on  in  the  other 
bulb  will  occasion  so  rapid  an  evaporation  as  to  cause  the  water 
to  freeze. 

Water  may  also  easily  be  made  to  freeze  by  the  evaporation  of 
sulphuric  ether.  For  this  purpose  a  glass  tube,  1  line  in  width, 
is  enclosed  in  cotton  wool  moistened  with  sulphuric  ether.  The 
tube  thus  prepared  is  placed  in  any  kind  of  glass  vessel,  and  put 
under  the  receiver  of  the  air-pump.  On  exhausting  the  air,  the 
ether  is  so  rapidly  evaporated  that  the  water  freezes. 

Freezing  of  Mercury. — We  may  carry  cooling  by  evaporation 
down  to  the  freezing  point  of  mercury.  To  effect  this  we  surround 
a  thermometer  bulb  with  a  sponge,  or  other  porous  tissue,  which 
must  be  moistened  with  sulphuret  of  carbon,  or  still  better,  with 
liquid  sulphurous  acid.  Evaporation  goes  on  so  rapidly,  and  the 
amount  of  heat  abstracted  is  so  great,  that  the  thermometer  falls 
to  14°  — 4°,  or  even—  22°,  and  the  mercury  in  the  bulb  freezes 
after  the  lapse  of  a  few  minutes. 

A  liquid  evaporates  more  rapidly,  consequently  generates  a 
greater  degree  of  cold  during  its  evaporation,  in  proportion  to  the 
lowness  of  its  boiling  point ;  on  this  account  a  greater  degree  of 
cold  is  produced  by  the  evaporation  of  sulphuric  ether  than  by 
water,  more  by  sulphurous  acid  than  by  ether,  and,  finally,  still 
more  by  liquid  carbonic  acid  than  by  sulphurous  acid. 


536  SPECIFIC    HEAT    OF    BODIES. 


CHAPTER    III. 

SPECIFIC  HEAT  OF  BODIES. 

Means  of  Comparing  Quantities  of  Heat. — We  assume  as  a 
self-evident  principle,  that  the  same  quantity  of  heat  must  always 
be  required  to  produce  the  same  effect.  If,  for  instance,  1  Ib.  of 
iron  at  50°  have,  from  any  cause,  been  heated  to  the  temperature 
of  51°,  the  same  quantity  of  heat  must  always  be  required, 
whether  the  source  be  the  sun,  or  a  fire ;  or  whether  it  reach  the 
iron  by  contact  or  by  radiation.  In  like  manner,  the  same  amount 
of  heat  will  always  be  required  to  fuse  1  Ib.  of  ice  at  32°,  and  a 
definite  quantity  to  evaporate  1  Ib.  of  water  at  212°.  The  quan- 
tities of  heat  must,  however,  also  be  proportional  to  the  weight  of 
the  substances  on  which  they  act,  in  order  to  produce  a  definite 
effect;  that  is,  to  raise  the  temperature  of  100  Ibs.  of  iron,  from 
50°  to  51° ;  and,  in  order  to  fuse  100  Ibs.  of  ice,  or  evaporate 
100  Ibs.  of  water,  a  hundredfold  greater  amount  of  heat  is  neces- 
sary than  is  required  to  produce  the  same  effect  on  1  Ib.  of  these 
substances. 

A  substance  has  a  greater  or  less  capacity  for  heat,  according 
as  a  greater  or  less  quantity  of  heat  is  required  to  produce  a 
definite  change  of  temperature,  or  an  elevation  of  temperature  of 
1°  ;  this  requisite  quantity  of  heat  is  termed  the  specific  heat  of 
the  substance.  Two  bodies  have  equal  capacities  of  heat,  if  of 
equal  weight ;  they  require  the  same  quantity  of  heat  to  raise  their 
temperature  1°;  on  the  contrary,  the  capacity  of  heat  of  a  body 
is  2,  3,  or  4  times  greater  than  that  of  another,  if  it  require  a  2, 
3,  or  4  times  greater  quantity  of  heat. 

One  and  the  same  body  may  have  a  variable  capacity  for  heat; 
as,  for  instance,  is  the  case  with  platinum,  which  requires  a 
greater  amount  of  heat  to  be  heated  from  212°  to  213°,  than  to 
raise  its  temperature  from  32°  to  33°.  The  capacity  of  water  for 
heat  is  constant,  on  which  account  this  liquid  has  been  chosen  as 
the  unit. 

From  these  definitions  it  follows,  that  a  body,  whose  weight  is 
m,  and  whose  capacity  for  heat  is  c,  will,  at  an  elevation  or  de- 


THE   METHOD   OF   MIXTURES.  537 

pression  of  temperature  of  £°,  receive  or  lose  an  amount  of  heat, 
the  product  of  which  may  be  expressed  by  m  c  t. 

In  order  to  determine  the  specific  heat  of  bodies,  three  different 
methods  have  been  pursued,  viz.,  that  of  the  fusion  of  ice,  mix- 
tures, and  cooling. 

According  to  the  first  method,  the  body  whose  specific  heat  is 
to  be  determined,  is  weighed,  heated  to  a  definite  temperature, 
and  placed  in  a  vessel  filled  with  pieces  of  ice.  While  it  cools, 
a  part  of  the  ice  is  fused,  and,  from  the  quantity  of  water,  we 
obtain  the  quantity  of  heat  lost  by  the  body,  and  hence,  conse- 
quently, its  specific  heat. 

The  cooling  method  is  based  upon  the  following  principle.  If 
a  heated  body  be  brought  into  a  space  in  which  it  can  only  cool 
by  radiation,  it  will,  if  other  circumstances  remain  the  same,  cool 
slower  in  proportion  to  the  amount  of  specific  heat. 

The  method  of  mixtures  affords  the  most  accurate  results,  and 
must,  therefore,  be  somewhat  more  attentively  considered.  This 
method  consists  principally  in  this;  a  weighed  quantity  of  the 
body  to  be  examined  is  heated  to  a  certain  temperature,  and  then 
plunged  into  a  vessel  with  water,  the  temperature  of  which  has 
been  raised  by  the  cooling  of  the  body;  if  we  know  the  quantity 
of  the  cold  water,  we  may  ascertain  the  elevation  of  temperature 
sustained  by  it  from  the  cooling  of  the  immersed  body,  and  thus 
the  specific  heat  of  the  latter  may  be  computed. 

If  we  assume  that  a  platinum  ball  weighing  200  grms.  (3088 
grs.),  warmed  to  212°,  has  been  immersed  in  a  mass  of  water  of 
105  grms.  (1621  grs.),  at  59°,  and  has  raised  its  temperature,  by 
its  own  cooling,  to  68°,  that  is,  has  heated  the  water  9°,  it  is 
clear,  that  the  200  grms.  (3088  grs.)  of  platinum  must  be  cooled 
down  to  176°,  in  order  to  heat  105  grms.  (1621  grs.)  of  water  9°. 
The  same  amount  of  heat  that  has  been  yielded  by  the  platinum 
ball  would,  therefore,  also  have  sufficed  to  raise  the  temperature 
of  525  grms.  (8108  grs.)  of  water  (1.8°).  If  the  platinum  ball 
had  only  weighed  1  grm.,  (15.444  grs.,)  the  amount  of  heat  given 
off  by  it,  at  a  depression  of  temperature  of  176°,  would  be  able  to 


warm  only  ™*9  (™j\  or  2,625  grms.  (grs.)  of  water  (1.8°),  or 

200   VoOoo/ 

1  grm.  (15.444  grs.)  of  water  2,625°.  Hence,  it  follows,  that 
the  same  amount  of  heat  that  raises  the  temperature  of  1  grm. 
(15.444  grs.)  of  platinum  176°,  can  only  raise  an  equal  mass  of 


538        RESULTS    OF    EXPERIMENTS    ON    SPECIFIC    HEATS. 

water  2,625°;  platinum  thus  requires  only  2'625,  that  is,  0,0328 

oU 

times  less  heat  than  an  equal  quantity  of  water,  to  experience  an 
equal  variation  of  temperature  ;  the  specific  heat  of  platinum  is, 
consequently,  0,0328. 

If  we  designate  the  weight  of  the  cooling  water  by  m,  and  the 
elevation  of  temperature  by  t,  (in  the  above-given  example  they 
were  105  grms.  (1621  grs.)  and  9°),  and  the  weight  and  depres- 
sion of  temperature  of  the  cooled  body  as  m  and  t',  (in  our  exam- 
ples they  stood  as  200  grms.  (3088  grs.)  of  platinum  and  176°,) 
it  follows  from  the  above-given  considerations,  for  a  concrete  case, 
that  we  have  the  following  formula  for  the  computation  of  the 


vn 


specific  heat  c  of  the  cooled  body  :  c  =  —  j—j  ;  that  is,  expressed 

ftv     L 

in  words,  we  find  the  specific  heat  of  the  cooled  body  by  dividing 
the  product  of  the  weight  of  the  cooling  water,  and  its  variation 
of  temperature  by  the  product  of  the  weight  of  the  body  and  its 
depression  of  temperature. 

Results  of  the  Experiments  on  Specific  Heats.  —  The  determina- 
tion of  specific  heat  has  acquired  much  importance  in  chemistry 
from  the  labors  of  Dulong  and  Petit,  who  found  that  the  product 
obtained  on  multiplying  the  specific  heat  of  an  element  by  its 
atomic  weight,  was  always  constant.  Thus,  for  instance,  they 
found  the  specific  heat  of  iron  to  be  equal  to  0,1100,  while  the 
atomic  weight  of  the  metal  was  339,2,  and  their  product  is  37,31. 
If  we  multiply  the  specific  heat  of  copper  0,0949  with  its  atomic 
weight  395,7,  we  obtain  the  product  37,55,  a  value  which  agrees 
almost  perfectly  with  what  has  been  found  for  iron.  In  like 
manner,  it  was  found  that  this  product  was  almost  exactly  the 
same  for  all  metallic  elements;  it,  therefore,  appears  that  the 
principle  of  the  specific  heat  of  metallic  elements  being  inversely 
proportional  to  their  atomic  weight,  is  well-grounded. 

We  have,  thus,  one  means  more  of  learning  to  know  the  atomic 
weight  of  a  body,  and  to  test  the  value  of  atomic  weights  found 
by  other  methods.  The  atomic  weights  of  the  elements  were  not, 
at  the  period  when  Dulong  and  Petit  carried  out  their  researches, 
as  firmly  established  as  at  present  ;  choice  had  often  to  be  made 
between  many  atomic  weights  for  the  same  body,  and  Dulong 
and  Petit  naturally  selected  the  one  most  in  harmony  with  their 
own  law. 


TRANSMISSION    OF    HEAT. 


539 


Subsequently  to  that  time,  atomic  weights  were  more  exactly 
determined  in  another  way ;  but  this,  instead  of  confirming  the 
law  of  Dulong,  seemed  rather  to  yield  results  in  direct  opposition 
to  those  obtained  by  his  method.  The  most  recent  investigations 
of  Regnault,  upon  specific  heat,  have,  however,  established  the 
correctness  of  this  law  beyond  all  doubt. 


CHAPTER    IV. 


TRANSMISSION    OF    HEAT. 

Existence  of  Radiating  Heat. — Radiating  heat  penetrates  cer- 
tain bodies  in  the  same  manner  as  light  passes  through  trans- 
parent bodies ;  the  rays  of  the  sun,  for  instance,  impinge  upon 
our  earth  after  they  have  traversed  the  whole  atmosphere,  and  heat 
the  earth's  surface,  whilst  the  higher  regions  of  the  air  remain 
cold  ;  the  rays  of  heat  consequently  pass  for  the  most  part  through 
the  atmosphere  without  being  absorbed  by  it.  On  approaching 
the  fire  of  a  hearth,  we  experience  a  burning  heat,  and  yet  the 
air  between  us  and  the  fire  is  not  heated  to  an  equal  degree,  for 
on  holding  up  a  screen  this  heat  instantaneously  ceases,  which 
could  not  possibly  be  the  case  if  the  whole  mass  of  air  surround- 
ing us  had  so  high  a  temperature.  Hot  bodies  can,  therefore, 
emit  heat  in  all  directions,  which  passes  through  the  air  as  the 
rays  of  light  through  transparent  bodies;  we,  therefore,  speak  of 
radiating  heat,  and  rays 


Fig.  506. 


of  heat,  in  the  same 
manner  as  rays  of  light. 
If  two  large  spheri- 
cal, or  parabolic  concave 
mirrors  of  polished  tin- 
plate  (Fig.  506),  be  re- 
moved about  10  or  12 
feet  from  each  other,  and 
so  placed  that  the  axes 
of  both  mirrors  fall  upon  the  same  line,  and  if  a  piece  of  tinder 


540  RUMFORD'S    DIFFERENTIAL    THERMOMETER. 

be  placed  in  the  focus  of  the  one  mirror,  and  an  iron  ball  in  a 
state  of  white  heat,  or  a  burning  coal,  whose  combustion  is  quick- 
ened by  a  bellows,  be  laid  in  the  opposite  focus,  the  tinder  will 
soon  ignite,  as  if  it  had  been  brought  into  contact  with  a  fire. 
This  experiment  proves  that  the  glowing  body  radiates  heat ;  for 
it  is  evident  that  the  tinder  has  not  been  ignited  by  the  intervening 
layers  of  air  having  become  by  degrees  so  strongly  heated.  On 
removing  the  tinder  from  the  focus,  it  will  not  be  ignited,  even  on 
being  brought  much  nearer  to  the  glowing  body. 

If  we  put  a  ball  at  560°  in  the  place  of  the  glowing  coal,  and 
a  common  thermometer  in  the  place  of  the  tinder,  the  thermo- 
meter will  rapidly  rise ;  consequently,  this  ball  at  560°  likewise 
radiates  heat. 

If,  instead  of  the  hot  ball  at  560°,  we  take  a  vessel  full  of 
boiling  water,  or  filled  with  water  at  190°,  170°,  or  160,  we  may 
not,  perhaps,  observe  any  further  elevation  of  temperature  in  the 
thermometer;  this,  however,  does  not  prove  that  the  walls  of  the 
vessel  radiate  no  more  heat  at  this  temperature,  but  merely,  that 
a  common  thermometer  is  not  sensitive  enough  for  this  purpose. 
More  sensitive  instruments  have,  therefore,  been  made  use  of,  as, 
for  instance,  an  air  thermometer,  Rumford's  or  Leslie's 
Fig.  507.  differential  thermometer,  or  MellonVs  thermo-multipli- 
cator. 

An  air  thermometer  may  be  constructed  for  this  pur- 
pose, somewhat  in  the  manner  represented  in  Fig.  507. 
A  bulb  of  from  1  to  1^  inch  in  diameter  is  blown  at 
the  end  of  a  tube,  the  bore  of  which  is  about  0.039  inch ; 
the  tube  is  bent,  as  may  be  seen  in  the  figure,  and  has 
in  the  middle  a  second  bulb,  and  at  its  other  extremity 
a  funnel,  in  order  to  prevent  the  fluid  standing  between 
c  and  d  from  returning  into  the  lower  bulb,  or  running 
out  at  the  top.  When  the  dimensions  of  the  instrument  are 
known,  we  may  easily  compute  almost  the  full  degree  of  its  sen- 
sitiveness ;  it  cannot,  however,  be  graduated,  owing  to  the  fluid 
remaining  exposed  to  the  atmospheric  pressure,  and  owing  to  the 
alternate  entrance  and  escape  of  air  from  the  lower  bulb. 

Rumford's  Differential  Thermometer. — Fig.  508  exhibits  an 
apparatus  consisting  of  two  glass  bulbs,  a  and  6,  connected  by 
a  bent  glass  tube,  whose  horizontal  part  is  from  15  to  18  inches 
in  length.  In  this  tube  there  is  an  index  of  alcohol,  or  sulphuric 


LESLIE'S    DIFFERENTIAL    THERMOMETER. 


541 


Fig.  508. 


Fig.  509. 

o      o 


acid,  pressed  upon  on  each  side  by  the  air  of  the  bulbs,  and  it 
will  consequently  only  stand  in  a 
fixed  position  when  the  pressure 
on  both  sides  is  equal.  The  place 
occupied  by  the  index  when  the 
temperature  of  both  bulbs  is  per- 
fectly equal,  is  the  zero  of  the 
division.  If  the  one  bulb  be 
heated  more  than  the  other,  the 
index  will  be  driven  towards  the 
cooler  bulb,  and  its  removal  from 
the  zero  will  be  proportional  to 
the  difference  of  temperature  of  the  two  bulbs. 

Leslie's  Differential  Thermometer. — Fig. 
509  is  constructed  in  a  similar  way,  with  the 
exception  of  having  somewhat  smaller  bulbs, 
and  the  vertical  arms  of  the  connecting  tubes 
being  longer,  and  nearer  to  each  other. 

Mellon? s  thermo-multiplicator  consists  of 
a  thermo-electric  pile,  Fig.  509,  such  as  has 
already  been  described  at  page  481,  and  of 
a  very  sensitive  multiplicator.  The  pile  is 
carefully  blackened  at  both  ends  with  soot, 
and  placed,  together  with  its  casing,  at  p 
(Fig.  511)  upon  a  stand ;  the  coverings  a  and 
b  serve  to  keep  the  currents  of  air  and  the 
lateral  radiations  from  the  pile  ;  as  the  one  b 
is  conical,  it  also  serves  to  concentrate  the 
rays  of  heat  from  this  side,  if  necessary.  The 
copper  wire  forming  the  galvanometer,  is  7 
or  8  yards  long,  and  is  wound  40  times  round  a  metal  frame. 
The  well  chosen  magnetized  needles,  after  having  been  carefully 
compensated,  are  connected  together,  as  seen  in  Fig.  512.  This 
system  is  suspended  by  a  cocoon  thread,  hanging  in  the  centre 
of  a  glass  bell  c,  Fig.  51 1.  By  turning  the  knob  /,  the  cocoon 
thread  may  be  somewhat  raised  or  lowered,  together  with  the 
needles.  The  apparatus  must  be  placed  upon  a  sufficiently 
strong  table,  and  at  a  proper  level,  so  that  the  thread  hangs 
exactly  in  the  middle  of  the  graduated  circle,  and  so  directed  that 
46 


/ 
c 

\       f 

cf 

Fig.  510. 


542  CAPACITY    OF    BO.DIES    TO    RADIATE    HEAT. 

Fig.  511. 


Fig.  512. 


the  needles  point  to  the  zero  of  the  scale,  when  their  plane  coin- 
cides with  the  magnetic  meridian. 

The  easily  expanding  wire  spirals,  g  and 
h,  which  are  in  connection  with  the  two  ends 
of  the  thermo-electric  pile  at  x  and  y,  and 
at  ra  and  n,  with  the  ends  of  the  multiplica- 
tor  wire,  serve  to  restore  the  connection  be- 
tween the    thermo-electric    pile,    and   the 
multiplicator.     The   smallest   difference  of 
temperature  between  both  blackened  ends  of  the  column  causes 
a  deviation  of  the  needle,  which  may  be  seen  by  the  graduated 
scale. 

Capacity  of  Bodies  to  Radiate  Heat. — The  capacity  possessed 
by  bodies  of  radiating  heat  is  very  dissimilar,  and  depends  essen- 
tially upon  the  condition  of  the  surface  ;  in  general  the  surfaces  of 
the  less  dense  bodies  radiate,  other  circumstances  being  the  same, 


ABSORPTION    OF    RAYS    OF    HEAT.  543 

more  heat  than  the  surfaces  of  bodies  possessing  a  greater  density. 
The  irregularity  in  the  capacity  of  radiation  of  different  surfaces, 
has  been  illustrated  by  Leslie  in  the  following  manner :  he  brought 
the  bulb  of  his  differential  thermometer  into  the  focus  of  a  con- 
cave mirror,  and  placed  at  some  distance  from  the  axis  of  a  mir- 
ror, a  hollow  tin-plate  cube,  filled  with  hot  water;  the  sides  of 
the  vessel  being  from  7  to  8  inches  in  length,  and  one  lateral 
side  being  covered  with  soot,  while  the  other  was  polished ;  when 
the  latter  side  was  turned  towards  the  mirror,  the  effect  was  much 
less  considerable  upon  the  differential  thermometer  than  when 
the  blackened  side  was  turned  towards  it ;  the  surface  rubbed  with 
soot,  consequently  radiated  far  more  heat  than  the  polished  metal- 
lic surface. 

This  method  is  certainly  quite  capable  of  showing  the  differ- 
ence in  capacity  of  radiation;  but  to  give  more  exact  compari- 
sons, however,  MellonVs  method  is  far  more  preferable ;  he 
placed  at  a  proper  distance  from  the  thermo-pile  a  hollow  cube 
of  tin  plate,  the  side  of  which  was  from  2J  to  3  inches  long,  and 
which  was  filled  with  hot  water,  kept  at  a  constant  temperature 
by  means  of  a  spirit  lamp ;  the  lateral  surfaces  of  this  cube  were 
differently  prepared,  one  being  covered  with  soot,  another  with 
white  lead,  the  third  with  Indian  ink,  and  the  remaining  one  po- 
lished. The  deviations  of  the  needle  were  very  unequal,  as  the 
one  or  the  other  side  was  turned  towards  the  thermo-multiplicator, 
and  from  the  deviations  thus  observed,  was  found  without  further 
difficulty,  the  relation  in  which  the  capacities  of  emission  stand 
to  each  other  for  different  fluids.  In  this  manner  the  capacity  of 
radiation  has  been  determined  for  the  following  bodies : 

Lamp-black  .         .  100  Indian  ink  .         .     85 

White  lead     .         .  100  Gum  lac      . 

Isinglass         .         .     91  Metallic  surface   .     12 

Thus,  if  we  designate  the  capacity  for  radiation  in  pine  soot 
as  100,  that  of  a  polished  surface  will  be  equal  to  12,  conse- 

12 

quently,  only of  the  former. 

100 

Absorption  of  Rays  of  Heat.— Every  body  has  the  power  of 
absorbing  more  or  less  the  rays  of  heat,  which  impinge  upon  it 
coming  from  some  other  body;  this  is  proved  in  the  above-named 
experiments,  for  bodies  are  only  heated  in  the  focus  of  a  concave 


544  REFLECTION   AND    DIFFUSION    OF    HEAT. 

mirror,  because  they  absorb  the  rays  of  heat  concentrated  upon 
them  by  the  mirrors.  That  this  power,  however,  appertains  to 
all  bodies,  is  proved  by  their  assuming  a  temperature  when 
exposed  to  the  sun's  rays,  which  is  higher  than  the  temperature 
of  the  air. 

The  power  of  absorption  is  not  equal  for  all  bodies,  which 
arises  from  their  not  having  equal  power  of  emission,  for  a  sur- 
face which  easily  radiates  heat  must,  conversely,  also  have  the 
capacity  for  absorbing  these  rays.  This  inequality  in  the  power 
of  absorption  may  be  shown  by  a  simple  experiment ;  for  instance, 
if  we  put  a  thermometer,  whose  bulb  has  been  blackened,  in  the 
rays  of  the  sun,  it  will  rise  much  more  rapidly  than  another, 
whose  surface  has  not  been  blackened ;  the  blackened  surface  of 
the  one  thermometer  bulb  absorbs,  therefore,  evidently  more  rays 
of  heat  than  the  polished  surface  of  the  other. 

The  rays  of  heat  absorbed  by  a  body  are,  therefore,  the  cause 
of  its  becoming  heated ;  and  thus,  in  order  to  heat  a  body  by 
radiation  as  much  as  possible,  it  is  necessary  to  cover  it  with 
some  coating,  which  strongly  absorbs  rays  of  heat ;  for  the  same 
reason,  thermoscopes,  which  serve  to  manifest,  in  a  striking 
manner,  the  actions  of  the  radiation  of  heat,  the  bulbs  of  differ- 
ential thermometers,  and  the  two  ends  of  the  thermo-electric  pile 
are  coated  over  with  soot,  as  this  substance  has  a  stronger  capacity 
for  absorption  than  any  other  with  which  we  are  acquainted. 

We  have  seen  above  that  metallic  surfaces  possess  only  a  very 
small  power  of  emission,  and  hence  it  follows  that  they  are  only 
capable  of  absorbing  rays  of  heat  to  a  very  small  degree. 

Reflection  and  Diffusion  of  the  Rays  of  Heat. — Bodies  have,  in 
general,  the  capacity  of  reflecting  a  portion  of  the  rays  of  heat 
impinging  upon  (hem  in  the  same  manner  as  they  more  or  less 
regularly  reflect  rays  of  light.  The  mirrors,  which  were  used  in 
the  above  experiments,  furnish  us  with  a  decisive  proof  of  the  re- 
flection of  rays  of  heat,  for  they  are  not  themselves  heated  in  the 
experiment  with  the  tinder.  A  simple  mode  of  reasoning  con- 
vinces us  that  most  bodies  must  possess  this  capacity  for  reflection, 
and  that,  if  we  may  so  speak,  it  is  complementary  to  the  power 
of  absorption,  for  the  sum  of  the  absorbed  rays  of  heat  must  evi- 
dently be  equal  to  the  combined  whole  of  the  incident  rays,  pro- 
vided the  body  suffer  no  rays  of  heat  to  pass  through  it.  When, 
therefore,  the  power  of  reflection  is  greater,  the  power  of  absorp- 


CAPACITY    OF    BODIES    TO    TRANSMIT    RAYS    OF   HEAT.      545 

tion  is  smaller,  and  conversely.  A  body  that  reflects  no  rays  of 
heat  must  absorb  all  rays,  as,  indeed,  is  the  case  with  such  sur- 
faces as  are  carefully  covered  with  soot ;  polished  metallic  surfaces, 
on  the  other  hand,  which  possess  a  great  capacity  of  reflection, 
only  absorb  rays  of  heat  to  a  very  inconsiderable  degree. 

Rays  of  heat  are  reflected  precisely  according  to  the  same  laws 
as  rays  of  light,  that  is  to  say,  the  angle  of  reflection  is  equal  to 
the  angle  of  incidence  ;  this  follows  from  the  experiments  with 
the  concave  mirrors,  as  the  focal  points  for  the  rays  of  heat  cor- 
respond with  those  of  the  rays  of  light. 

As  rays  of  light  are  irregularly  distributed  in  all  directions  on 
the  surface  of  a  perfectly  polished  body,  rays  of  heat  likewise 
undergo  a  diffusion  on  the  surface  of  most  bodies.  We  may  con- 
vince ourselves  of  this  by  the  following  experiment.  If  we  suffer 
the  sunbeams  to  fall  through  an  opening  in  the  shutter  of  a  dark 
room  upon  the  opposite  wall,  the  luminous  spot,  which  is  visible 
from  all  directions,  owing  to  its  distributing  sunlight  on  every 
side,  will  also  distribute  rays  of  heat  irregularly,  that  is,  it  will 
throw  forth  rays  of  heat  in  all  directions,  as  if  it  were  itself  a 
source  of  heat.  This  diffusion  of  the  rays  of  heat  is  rendered 
manifest  on  turning  the  thermo-electric  pile  towards  the  bright 
spot;  we  shall  see  the  needle  deviate  at  whatever  part  of  the 
room  we  place  the  instrument ;  and  the  action  cannot,  therefore, 
arise  from  a  regular  reflection,  while  it  is  evident,  that  it  is  not 
the  consequence  of  a  heating  of  the  part  of  the  wall  on  which  the 
sun's  rays  have  fallen,  for  the  needle  will  return  to  the  zero  of  the 
scale  as  soon  as  the  aperture  in  the  shutter  is  closed. 

Capacity  of  Bodies  to  transmit  Rays  of  Heat. — That  solid  bodies 
can  transmit  rays  of  heat  in  the  same  manner  that  transparent 
bodies  transmit  rays  of  light,  has  already  been  proved,  by  showing 
that  we  are  able  to  ignite  combustible  bodies  on  holding  them  in 
the  focus  of  a  lens  exposed  to  the  rays  of  the  sun.  More  accurate 
investigations  could  only  be  made  by  help  of  the  thermo-electric 
pile,  and  Melloni  has  carried  out  a  series  of  highly  interesting  ob- 
servations upon  the  transmission  of  the  rays  of  heat  through  differ- 
ent bodies. 

Such  bodies  as  retain  rays  of  heat  as  transparent  bodies  retain 
rays  of  light,  are  termed  by  Melloni,  athermanous;  and  those 
which  are  to  rays  of  heat  as  transparent  bodies  are  to  rays  of  light, 

46* 


546      CAPACITY    OF    BODIES    TO    TRANSMIT    RAYS    OF    HEAT. 

are  called  by  him  diathermanous.  Air,  consequently,  is  a  diather- 
manous  body ;  ancl  we  shall  soon  see  that  many  solid  and  fluid 
bodies  are  diathermanous,  although  in  very  unequal  degrees. 

The  experiments  were  made  in  the  following  manner. 

The  source  of  heat,  a  small  oil  lamp,  for  instance,  or  a  hollow 
cube  of  tin  plate  filled  with  hot  water,  and  blackened  on  the  out- 
side writh  soot  to  radiate  heat  the  better,  was  so  placed  as  to  pro- 
duce a  deviation  of  the  needle  of  30°;  when  the  rays  of  heat  were 
then  received  upon  a  plate  of  the  body  to  be  examined,  and 
placed  at  r,  Fig.  509,  the  needle  receded  sometimes  more,  some- 
times less,  and  it  was  thus  observed  that  equally  thick  and  equally 
transparent  plates  of  different  bodies  did  not  transmit  equal  quan- 
tities of  radiating  heat.  If,  for  instance,  the  free  radiation  of  the 
source  of  heat  cause  a  deviation  of  30°,  the  needle  will  recede  to 
28°  if  a  plate  of  rock  salt  from  0.11  to  0.15  of  an  inch  in  thick- 
ness be  placed  at  r,  whilst  an  equally  thick  plate  of  quartz  will 

Fig.  513. 


DISTRIBUTION   OF    HEAT   BY   CONDUCTORS.  547 

cause  the  needle  to  recede  to  15  or  16°;  mineral  or  rock  salt,  con- 
sequently, transmits  rays  of  heat  far  better  than  rock  crystal. 
Many  less  transparent  bodies  even  transmit  rays  of  heat  better 
than  those  that  are  perfectly  transparent.  Whilst,  for  instance,  a 
wholly  transparent  plate  of  alum  reduces  the  deviation  of  the 
needle  from  30°  to  3  or  4°,  a  far  thicker  plate  of  smoky-topaz 
brings  the  needle  back  to  14  or  15°.  Some  bodies  which  are 
almost  wholly  opaque,  as  black  glass  and  black  mica,  transmit 
rays  of  heat  tolerably  well. 

If  we  suffer  the  rays  of  heat  that  have  passed  through  a  glass 
plate  to  fall  upon  an  alum  plate,  they  will  be  wholly  absorbed ; 
whilst,  however,  an  alum  plate  will  transmit  almost  all  the  rays  of 
heat  that  had  previously  passed  through  a  plate  of  citric  acid. 
This  phenomenon  has  the  greatest  analogy  with  the  transmission 
of  light  through  a  colored  medium;  rays  of  light  that  have 
passed  through  green  glass  are,  it  is  well  known,  easily  transmit- 
ted through  other  green  glasses,  which  are  absorbed  when  suffered 
to  fall  upon  red  glass ;  the  differences  between  rays  of  heat  are, 
therefore,  quite  analogous  to  the  differences  of  color  in  light. 

Similar  resemblances  have  been  observed  in  relation  to  the 
capacity  of  emission  and  absorption  of  bodies. 

Rays  of  heat  are  refrangible,  like  rays  of  light,  as  may  best  be 
seen  by  means  of  a  prism  of  rock  salt.  Phenomena  of  polariza- 
tion have  also  been  shown  in  rays  of  heat. 

Distribution  of  Heat  by  Conductors. — Heat  may  pass  from  one 
body  to  another,  not  only  by  radiation,  but  by  immediate  contact, 
and  may  then  be  transmitted  through  the  whole  mass;  there  is, 
however,  a  great  inequality  in  different  bodies  in  relation  to  the 
facility  with  which  this  is  effected  ;  in  many,  heat  is  very  easily 
transmitted,  whilst  in  others  it  passes  with  much  less  facility  from 
one  particle  to  another.  A  match  that  is  burning  at  one  end  may 
be  held  between  the  fingers  at  the  other  extremity  without  any 
elevation  of  temperature  being  even  felt  in  the  wood ;  the  high 
temperature  of  the  burning  end  is  not  speedily  transmitted  to  the 
rest  of  the  mass  of  wood,  because  wood  is  a  bad  conductor  of 
heat.  An  equally  long  metallic  wire  made  glowing  hot  at  one 
extremity  cannot  be  grasped  at  the  other  end  without  burning  the 
hand;  heat,  consequently,  distributes  itself  from  the  glowing  part 
to  the  whole  of  the  rod,  metal  being  a  good  conductor. 


548         LIQUIDS    AND    GASES    AS    CONDUCTORS    OF    HEAT. 

We  may  make  use  of  Ingenhousz's  apparatus  (Fig.  514)  to  show 
Fig  514  the  inequality  of  the  capacity  of  different 

bodies  to  transmit  heat.  Many  rods  made 
of  the  substances  to  be  compared  are  in- 
serted into  the  lateral  wall  of  a  box  of 
tin  plate,  the  rods  being  all  of  equal 
diameter,  and  all  covered  with  a  layer  of  wax;  on  pouring  boiling 
water  or  hot  oil  into  the  box,  the  heat  will  penetrate  more  or  less 
into  the  rods  and  fuse  the  wax  coating.  If  we  assume  that  one 
rod  is  of  copper,  another  of  iron,  a  third  of  lead,  a  fourth  of  glass, 
and  the  last  of  wood,  the  wax  coating  of  copper  will  be  perfectly 
fused  before  the  coatings  over  the  other  rods  are  much  melted, 
showing  that  copper  is  the  best  conductor  of  these  five  bodies. 
The  fusion  of  the  wax  is  more  rapid  over  the  iron  than  the  lead, 
and  when  all  the  wax  has  melted  off  the  copper  rod,  fusion  has 
only  progressed  to  a  very  small  extent  upon  the  glass  rod,  while 
scarcely  a  trace  of  fusion  is  perceptible  on  the  wooden  rod ;  which 
proves  that  wood  is  the  worst  conductor  of  heat  among  these  five 
substances. 

Of  all  bodies,  metals  are  the  best  conductors  of  heat ;  and 
ashes,  silk,  hair,  straw,  wood,  &c.,  and  porous  bodies  especially, 
are  the  wrorst. 

In  practical  life  we  are  constantly  making  numerous  applica- 
tions of  the  good  or  bad  capacity  of  different  bodies  for  conducting 
heat.  Thus,  objects  that  we  wish  to  protect  from  the  cold,  we 
surround  with  bad  conductors  of  heat:  twisting  straw  round  trees 
and  shrubs  in  winter  to  save  them  from  the  effect  of  the  frost;  on 
the  same  principle  our  clothes  keep  us  warm,  owing  to  their  being 
made  of  bad  conductors  of  heat.  We  can  bring  a  liquid  to  a  state 
of  boiling  much  more  rapidly  in  a  copper  vessel  than  in  one  made 
of  porcelain,  and  having  equally  thick  walls. 

Capacity  of  Liquids  and  Gases  for  conducting  Heat. — Heat  is 
distributed  through  liquids  principally  by  currents,  which  arise 
from  the  heated  particles  rising  more  rapidly  to  the  surface,  owing 
to  their  inconsiderable  density.  These  currents  may  be  made 
apparent  by  throwing  shavings  into  water  enclosed  in  a  glass  ves- 
sel, and  then  heating  it  slowly  from  below  (Fig.  515),  when  we 
shall  see  the  current  rise  in  the  middle,  and  be  directed  upwards, 
and  turn  downwards  on  either  side.  On  heating  a  liquid  from 
above,  so  that  the  hydrostatic  equilibrium  is  not  disturbed,  the 


LIQUIDS    AND    GASES    AS    CONDUCTORS    OF    HEAT.         549 


Fig.  515. 


heat  can  only  be  transmitted  in  the  same  manner  through  the 

mass  of  the  liquid,  as  is  the  case  with 

solid  bodies  ;  that  is  to  say,  by  the  heat 

being  conducted  from  one  layer  to  the 

other.      In  such    cases,    heat   is   only 

slowly  diffused  through  the  mass  of  the 

liquid  ;  liquids,  consequently,  are  bad 

conductors  of  heat. 

In  order  to  convince  one's  self  of  the 
bad  capacity  of  liquids  for  conducting 
heat,  one  need  only  plunge  the  bulb  of 
a  thermometer  into  cold  water,  and  then 
pour  hot  oil  upon  the  water.  The  up- 
permost layers  of  water  will  scarcely 
manifest  any  elevation  of  temperature. 

Despretz  has  determined  the  capacity 
of  liquids  for  conducting  heat,  by  heat- 
ing columns  of  water  1  metre  (yard) 
in  height  and  from  0,2  to  0,4  metres  (6 
to  12  inches)  in  diameter,  by  continually 

pouring  hot  water  over  them  from  above.  This  process  was  con- 
tinued for  about  30  hours,  until  the  temperature  of  the  columns 
was  settled  and  stable  on  all  sides.  From  these  experiments  it 
follows  that  the  capacity  of  water  for  conducting  heat  is  about  96 
times  less  than  that  of  copper. 

The  air  and  gases  especially  are  likewise  very  bad  conductors 
of  heat ;  but  we  are  unable,  owing  to  the  radiation  of  heat,  to 
ascertain  their  capacity  for  conducting  heat,  by  means  of  the 
thermometer  brought  into  the  different  layers  of  the  mass  of  air  to 
be  examined.  That  gases  generally,  and  the  air  in  particular, 
are  bad  conductors  of  heat,  is,  however,  proved  by  this :  that 
bodies  surrounded  on  all  sides  by  layers  of  air,  can  only  be  cooled 
or  heated  very  slowly,  if  only  the  intermixture  of  the  layers  of  air 
be  prevented.  We  thus  see  the  utility  of  double  windows  and 
double  doors  in  keeping  a  room  warm.  The  bad  capacity  for 
conducting  heat  which  we  perceive  in  porous  bodies,  as  straw, 
wool,  &c.,  depends  especially  upon  their  innumerable  interstices 
being  filled  with  air.  Bodies,  which  we  say  keep  us  warm,  as, 
for  instance,  our  clothes,  straw,  &c.,  are  not  warm  in  themselves, 
but  owe  the  property  they  possess  to  their  bad  power  of  conduct- 


550     GENERATION    OF    HEAT    BY    CHEMICAL    COMBINATIONS. 

ing  heat ;  if  we  wrap  any  of  these  round  ice,  they  will  hinder  its 
fusion,  by  protecting  it  from  all  external  heat. 


CHAPTER   V. 


Fig.  516. 


DIFFERENT    SOURCES    OF   HEAT.* 

Generation  of  Heat  by  Chemical  Combinations. — Excepting  the 
sun,  chemical  combinations  furnish  us  with  the  most  important 
sources  of  heat.  Almost  every  chemical  process  is  accompanied 
by  a  development  of  heat. 

The  development  of  heat  induced  by  combustion,  that  is,  by  a 
rapid  combination  of  bodies  with  oxygen,  is  of  the  greatest  im- 
portance. 

In  order  to  determine  the  amount  of  heat  developed  in  combus- 
tion, Rumford  made  use  of  the  apparatus  delineated  in  Fig.  516. 

The  box  JL  is  filled  with  water, 
through  which  passes  a  worm 
tube ;  the  entrance  of  this  tube 
is  formed  by  a  funnel,  below 
which  are  placed  the  bodies  to 
be  consumed.  The  experi- 
ment is  easily  made  with  oil 
and  alcohol,  which  are  poured 
into  a  little  lamp,  which  must 
be  weighed  at  the  beginning 
and  end  of  the  experiment,  in 
order  to  ascertain  the  quantity 
of  the  material  consumed. 
The  flame  and  the  products  of 
combustion  pass  through  the 
tube,  and  heat  the  water  of  the 

apparatus.     From  the  elevation  of  temperature  experienced  by 
the  water,  together  with  the  whole  apparatus,  we  may  estimate 


*  Thomson's  "Heat  and  Electricity,"  2d  edition,  8vo.,  1840. 


ANIMAL    HEAT.  551 

the  amount  of  heat  engendered  by  combustion;  but  here  we  must 
not  disregard  the  heat  carried  off  by  the  gaseous  products  of  com- 
bustion from  the  tube. 

By  experiments  of  this  kind,  the  following  results  were  obtained 
as  to  the  amount  of  heat  developed. 

By  the  combustion  of  1  grm.  The    temperature   of  1    kilogramme 

(15.444  grs.)  of  (2.679  Ib.)  of  water  may  be  raised 

Hydrogen 65,32° 

Olefiant  gas 20,96 

Absolute  alcohol     ....  12,52 

Charcoal 13,12 

Wax 18,90 

Rapeseed  oil  ....  16,75 

Tallow 15,06 

Animal  Heat. — The  temperature  of  the  heat  of  blood  of  all  ani- 
mals is  almost  always  different  from  that  of  the  medium  in  which 
they  live.  The  animals  of  the  polar  regions  are  always  warmer 
than  the  ice  on  which  they  live ;  but  in  the  countries  on  the 
equator  they  are  cooler  than  the  glowing  air  which  they  inhale. 
Neither  birds  nor  fish  have  the  same  temperature  as  the  air  or  the 
water  surrounding  them ;  the  animal  body  must  consequently  have 
a  peculiar  heat,  which  it  is  constantly  able  to  engender. 

The  internal  heat  of  the  human  body  appears  to  be  the  same 
for  all  organs,  and  to  be  equal  to  that,  to  which  a  small  thermo- 
meter rises,  when  we  place  the  bulb  under  the  tongue,  and  close 
the  mouth,  until  it  has  ceased  to  rise ;  this  temperature  is  about 
98°  F.  Age,  climate,  health,  and  disease,  can  but  slightly 
affect  it. 

The  blood  heat  is  greater  in  birds  than  in  any  other  animals, 
amounting,  on  an  average,  to  107.6°;  the  blood  heat  of  the  mam- 
malia is  very  nearly  equal  to  that  of  man.  In  birds  and  the 
mammalia,  the  blood  heat  is  independent  of  the  temperature  sur- 
rounding it ;  but,  in  other  species  of  animals,  as  the  amphibia, 
fishes,  &c.,  the  temperature  of  the  body  varies  but  little  from  the 
surrounding  medium. 

What,  then,  is  the  source  of  animal  heat?  The  air  which  we 
inhale  becomes  changed  in  the  same  manner  as  the  air  that  has 
served  in  the  combustion  of  bodies;  the  oxygen  being  converted 
into  carbonic  acid,  and  a  regular  process  of  combustion  being 


552      DEVELOPMENT    OF    HEAT    BY   MECHANICAL   MEANS. 

thus  carried  on  in  the  lungs.  Since  Lavoisier  made  this  disco- 
very, the  source  of  animal  heat  has  ceased  to  be  a  mystery.  Car- 
bon is  brought  into  the  body  with  the  food,  and  is  then  combined 
in  the  lungs  with  the  oxygen  of  the  inhaled  air.  By  the  oxidation 
of  carbon  in  the  animal  body,  the  same  amount  of  heat  must,  how- 
ever, necessarily  be  engendered  as  if  the  carbon  had  been  con- 
verted, by  rapid  combustion,  into  carbonic  acid. 

In  a  cold  medium,  men  and  animals  constantly  lose  more  heat 
than  in  a  warmer  atmosphere ;  as,  however,  the  blood  heat  in  the 
mammalia  and  in  birds  is  independent  of  the  temperature  of  the 
air,  it  is  evident  that  more  heat  must  be  engendered  in  the  body 
if  a  greater  quantity  be  withdrawn  every  moment  from  it,  and 
more,  consequently,  when  the  body  is  in  a  colder  air,  than  when 
it  gives  forth  but  little  heat  in  a  warmer  medium.  In  order,  how- 
ever, to  be  able  to  engender  more  heat  in  the  same  periods  of 
time,  more  carbon  must  be  introduced  into  the  body,  by  the  oxi- 
dation of  which  substance  heat  is  developed  :  in  the  same  manner 
as  we  must  consume  more  fuel  in  a  stove  during  cold  weather 
than  during  a  less  intense  degree  of  cold,  in  order  to  maintain  a 
constant  and  fixed  temperature  in  the  apartment.  Thus,  too,  we 
may  understand  why  the  inhabitants  of  northern  countries  require 
to  partake  of  more  food,  and  especially  of  the  kind  containing  a 
greater  amount  of  carbon,  than  is  necessary  for  those  who  live  in 
hotter  zones. 

Development  of  Heat  by  Mechanical  Means. — We  have  already 
stated  that  heat  is  liberated  by  the  compression  of  air ;  and  when 
this  is  rapidly  effected,  a  very  considerable  elevation  of  tempera- 
ture may  be  brought  about,  on  which  depends  the  pneumatic 
tinder-box.  Fluids  that  do  not  admit  of  strong  compression,  show 
but  an  inconsiderable  elevation  of  temperature.  Solid  bodies  are 
often  very  much  heated  by  compression,  as  we  may  observe  in 
the  case  of  hammering  metals  and  striking  coins.  It  has  not  yet 
been  determined  with  certainty,  whether  the  elevation  of  the  tem- 
perature of  solid  bodies,  by  compression,  must  likewise  be  ascribed 
to  the  circumstance,  that  their  heat  is  smaller  with  a  greater  de- 
gree of  density,  and  that,  consequently,  a  part  of  the  heat,  which 
is  maintained  in  them,  as  specific  heat,  escapes  in  a  perceptible 
form  on  their  being  compressed. 

The  considerable  elevations  of  temperature  occasioned  by  fric- 
tion are  generally  known.  The  iron  tire  of  a  wheel  often  becomes 


THEORETICAL    VIEWS    CONCERNING   HEAT.  553 

so  heated  that  it  will  hiss  on  coming  into  contact  with  water ;  dry 
wood  may  be  ignited  by  friction,  and  an  iron  nail  may  be  brought 
into  a  state  of  white  heat  on  being  held  against  a  moving  grind- 
stone of  7J  feet  in  diameter.  At  the  present  time,  we  are  unable 
to  afford  a  satisfactory  explanation  of  these  phenomena. 

Theoretical  Views  concerning  Heat* — We  have  become  ac- 
quainted with  the  most  important  laws  of  the  phenomena  of  heat, 
without  having  entered  upon  the  question  of  what  heat  really  is.f 
In  this  respect,  therefore,  the  theory  of  heat  has  been  treated  pre- 
cisely in  the  same  manner  as  the  first  part  of  the  theory  of  light, 
where  the  empirical  laws  of  reflection  and  refraction  were  deve- 
loped, without  anything  further  being  said  of  the  nature  of  light. 
We  are,  however,  still  deficient  in  a  theory  from  which  the  phe- 
nomena of  heat  may  be  derived  (as  the  phenomena  of  light  from 
the  wave  theory),  not  only  qualitatively,  but  also  quantitatively. 

We  generally  imagine  that  heat  is  an  imponderable  substance, 
penetrating  bodies:  and  this  idea  answers  very  well  for  many 
phenomena ;  as,  for  instance,  the  combination  of  heat,  and  the 
capacity  for  conducting  heat,  affording  us  a  good  representation 
of  these  phenomena,  the  expressions  being  based  upon  this  view. 
If,  however,  the  phenomena  of  the  capacity  for  conducting  heat, 
of  latent  heat,  and  of  diffusion  of  heat,  accord  tolerably  well  with 
the  idea  of  a  substance  of  heat,  it  is,  on  the  other  hand,  very  im- 
probable that  there  are  such  substances,  and  more  likely  that 
imponderables  will  all  vanish  from  physics,  as  has  already  been 
the  case  with  respect  to  light.  In  the  theory  of  heat,  the  most 
important  step  made,  is,  probably,  that  which  corresponds  to  the 
introduction  of  the  theory  of  vibration  in  the  case  of  light. 

There  are  some  phenomena  which  cannot  be  reconciled  with 
the  views  of  heat  being  a  substance;  for  instance,  radiation  and 
the  generation  of  heat  by  friction. 

The  laws  of  the  radiation  of  heat  are  so  similar  to  those  of  the 
radiation  of  light,  that  we  are  tempted  to  ascribe  the  former  like- 
wise to  a  vibration  of  ether.  If,  however,  radiating  heat  were 
:ransmitted  by  the  vibrations  of  ether,  perceptible  heat  must  like- 
wise be  occasioned  by  the  vibrations  of  the  material  parts  of 
)odies. 

*  Graham's  "Elements  of  Chemistry,"  2d  edition,  8vo.  1847. 
t  Thomson's  "Heat  and  Electricity,"  2d  edition,  8vo.  1840. 
47 


554  THEORETICAL    VIEWS    CONCERNING    HEAT. 

That  the  phenomena  of  heat  actually  arise  from  such  vibrations, 
is  very  probable,  although  we  are  not  able,  even  in  a  satisfactory 
degree,  to  explain  all  phenomena  of  heat  on  this  hypothesis ;  and 
we  are  still  unable  to  dispense  with  the  idea  of  a  substance  of  heat 
in  our  representations  and  descriptions. 

In  order  to  explain  the  phenomena  of  heat  by  vibrations,  we 
must  assume,  that  the  temperature  of  bodies  increases  with  the 
amplitude  of  the  oscillations ;  and  by  such  means  we  may  also 
explain  expansion  by  heat. 

The  number  of  the  vibrations  is  increased  on  the  transition  from 
the  solid  to  the  fluid,  and  from  the  latter  to  the  gaseous  condition. 
An  increase  in  the  number  of  the  vibrations  is,  with  an  equal 
amount  of  motion,  alone  possible  when  the  amplitude  is  less ;  and 
thus  we  may  explain  the  combination  of  heat. 


METEOROLOGY.  555 


SECTION  VIII. 

METEOROLOGY.* 


CHAPTER  I. 

DISTRIBUTION  OF  HEAT  ON  THE  EARTH'S  SURFACE. 

THE  heating  of  the  earth's  surface,  and  of  the  atmosphere,  by 
which  alone  the  vegetable  and  animal  world  can  thrive,  is  alone 
owing  to  the  rays  of  the  sun,  which  must  thus  be  regarded  as  the 
source  of  all  life,  upon  our  planet.  Where  the  mid-day  sun  stands 
vertically  above  the  heads  of  the  inhabitants,  and  its  rays  strike 
the  earth's  surface  at  a  right  angle,  a  luxuriant  vegetation  is 
developed,  if  a  second  condition  of  its  existence,  namely,  mois- 
ture, be  not  wanting ;  but  where  the  solar  rays  constantly  fall  too 
obliquely  to  produce  any  marked  effect,  nature  is  chained  in 
eternal  ice,  and  all  animal  and  vegetable  life  ceases. 

In  order  to  take  a  general  survey  of  the  distribution  of  heat 
on  the  earth's  surface,  we  must,  in  the  first  place,  investigate 
the  consequences  produced  by  the  diurnal  and  annual  motion  of 
the  earth. 

In  consequence  of  the  annual  motion  of  the  earth,  the  sun 
continually  alters  its  apparent  position  in  the  heavens;  the  path 
which  it  traverses,  during  the  year,  passes  through  twelve  con- 
stellations, called  the  signs  of  the  zodiac. 

If  we  suppose  the  vault  of  heaven  to  be  one  large  concave 
sphere,  the  path  of  the  sun  will  describe  a  large  circle  upon  it, 

>  The  want  of  space  prevents  this  important  subject  being  treated  as  fully  here 
as  it  deserves.  The  reader  is,  therefore,  referred  to  the  excellent  translation  of 
KAEMTZ'S  Complete  Course  of  Meteorology,  with  Notes  by  C.  V.  Walker,  illustrated 
with  15  plates.  London,  1845. 


556    DISTRIBUTION    OF    HEAT    ON    THE    EARTH'S    SURFACE. 

generally  known  by  the  name  of  the  elliptic.  This  line  does  not 
coincide  with  the  celestial  equator,  intersecting  it  at  an  angle  of 
23°  28'. 

Twice  in  the  year,  namely,  on  the  21st  of  March,  and  on  the 
21st  of  September,  the  sun  passes  the  celestial  equator.  From 
March  till  September  it  is  on  the  north,  and  from  September  to 
March  on  the  south,  hemisphere;  on  the  21st  of  June  it  reaches 
its  most  northern,  and  on  the  21st  of  December  its  most  southern, 
point ;  being,  on  the  first-named  day,  at  23°  28'  north,  and  the 
last-named,  at  23°  28'  south,  of  the  celestial  equator. 

The  direction  of  our  earth's  axis  coincides  with  the  axis  of  the 
heavens,  the  plane  of  the  terrestrial  equator,  with  that  of  the 
celestial  equator ;  if,  therefore,  the  sun  stand  directly  upon  the 
celestial  equator,  its  rays  strike  the  earth's  surface  at  every  place 
upon  the  terrestrial  equator  perpendicularly  at  mid-day,  whilst 
they  only  glance  over  the  two  terrestrial  poles,  striking  the  parts 
contiguous  to  them  very  obliquely. 

If  we  suppose  two  circles  to  be  drawn  upon  the  earth's  surface 
parallel  with  the  equator,  one  23°  28'  north,  and  the  other  equally 
far  south  of  it,  the  former  will  be  the  tropic  of  Cancer,  and  the 
latter  the  tropic  of  Capricorn.  All  places  lying  upon  these  tropics 
receive  once  in  the  year  the  sun's  rays  perpendicularly,  this  being 
on  the  21st  of  June  for  the  tropic  of  Cancer,  and  the  21st  of 
December  for  the  tropic  of  Capricorn. 

The  whole  terrestrial  zone  lying  between  those  two  tropics  is 
termed  the  hot  zone,  because  the  rays  of  the  sun  falling  but  very 
little  obliquely,  are  able  here  to  produce  the  most  powerful  effect. 

Heat  is  tolerably  equally  distributed  throughout  the  whole  year 
on  the  equator,  because  the  sun's  rays  strike  the  earth  rectangu- 
larly twice  annually,  while  they  do  not  fall  very  obliquely  at  any 
time  intervening  between  these  periods. 

The  more  we  approach  the  tropics,  the  more  marked  are  the 
differences  of  temperature  at  different  periods  of  the  year.  In 
the  tropics,  the  solar  rays  only  fall  once  in  the  year  perpendicularly 
on  the  .earth's  surface,  and  once  they  make  an  angle  of  47°  with 
the  direction  of  the  plumb  line,  falling,  consequently,  with  very 
considerable  obliquity ;  the  temperatures  of  the  hottest  and  coldest 
season,  separated  by  a  period  of  half  a  year,  differ  very  consider- 
ably from  each  other. 


DISTRIBUTION    OF   HEAT    ON    THE    EARTH'S    SURFACE.   557 

On  either  side  of  the  hot  zone,  extending  from  the  tropics  to 
the  polar  zones,  (the  polar  zones  are  those  which  have  24  hours 
exactly  for  their  longest  day,  and  lie  exactly  66°  32'  north  and 
south  of  the  equator,)  are  the  northern  and  southern  temperate 
zones  ;  the  four  seasons  of  the  year  are  most  strongly  characterized 
in  these  zones ;  in  general,  heat  diminishes  with  the  distance  from 
the  equator. 

Around  the  poles,  extending  to  the  polar  tropics,  are  the  north- 
ern and  southern  frigid  zones. 

In  consequence  of  the  rotation  of  the  earth  upon  its  axis,  the 
sun  appears  to  participate  in  the  apparent  motion  of  all  the  pla- 
nets ;  and  another  result  of  this  diurnal  motion,  is  evidently  the 
alternation  between  day  and  night.  It  is  only  during  the  former 
period  that  the  solar  rays  warm  the  earth's  surface,  which,  after 
sunset,  radiates  heat  towards  the  heavens,  without  the  loss  of  heat 
being  compensated  for;  during  the  night,  therefore,  the  surface 
of  the  earth  must  be  cooled. 

Under  the  equator  the  day  and  night  are  equal  throughout  the 
year,  each  day  and  night  lasting  12  hours;  as  soon,  however,  as 
we  remove  from  the  equator,  the  length  of  the  day  varies  with  the 
season  of  the  year,  the  variation  becoming  more  striking  as  we 
approach  nearer  to  the  poles.  The  following  table  contains  the 
length  of  the  longest  day  for  different  geographical  latitudes : 

Polar  elevation.  Length  of  the  longest  day. 

0  ....     12  hours. 

16°  44'  .         .         .         .     13     « 

30°  48'  .         .         .         .     14     " 

49°  22'  .         .         .         .16     " 

63°  23'  .         .         .         .20     " 

66°  32'  .         .         .         .24     " 

67°  23'  .         .         .         .       1  month. 

73°  39'  .         .         .         .3  months. 

90°  ....       6     u 

At  the  equator,  therefore,  the  variation  in  the  day's  length  can- 
not exercise  any  influence  upon  the  course  of  the  heat  in  the  dif- 
ferent seasons  of  the  year.  As  the  inequality  in  the  length  of  the 
days  is  not  very  considerable  even  under  the  tropics,  the  variation 
in  the  length  of  the  day  between  the  tropics  cannot  very  much 

47* 


558    DISTRIBUTION    OF    HEAT    ON    THE    EARTH'S    SURFACE. 

increase  or  diminish  the  differences  of  temperature  between  the 
hot  and  cold  seasons  of  the  year ;  this  is  the  case,  to  a  very  con- 
siderable degree,  in  high  latitudes. 

In  summer,  when  the  sun's  rays  fall  less  obliquely,  the  sun 
remains  longer  above  the  horizon  in  high  latitudes;  this  longer 
period  compensates  for  what  is  lost  in  intensity  by  the  solar  rays, 
and  it  thus  happens  that  it  may  be  very  hot  during  the  summer 
even  at  places  which  are  far  removed  from  the  equator,  (at  St. 
Petersburgh,  for  instance,  the  thermometer  sometimes  rises  in  a 
hot  summer  to  86° ;)  in  the  winter,  on  the  other  hand,  when  the 
more  obliquely  falling  solar  rays  have  only  little  power  of  acting, 
the  day  is  very  short,  and  the  night,  during  which  period  the  earth 
radiates  its  heat,  extremely  long ;  in  consequence  of  which,  the 
temperature  must  fall  very  low  at  this  season.  The  difference 
between  the  temperature  of  summer  and  winter  will,  therefore, 
generally  be  greater  the  further  we  remove  from  the  equator. 

At  Bogota,  which  is  4°  35'  N.  of  the  equator,  the  difference  of 
temperature  between  the  hottest  and  coldest  month  amounts  only 
to  3°;  in  Mexico  (19°  25'  N.  lat.)  this  difference  is  14°,  at  Paris 
(48°  50'  N.  lat.)  48°,  and  for  St.  Petersburgh  (59°  56'  N.  lat. 
57°. 

From  the  above  indicated  considerations,  it  follows,  therefore : 

1.  That  heat   must   diminish  from   the  equator  towards  the 
poles. 

2.  That,  in  the  vicinity  of  the  equator,  heat  is  distributed  tole- 
rably equally  over  the  whole  year;  that,  consequently,  the  charac- 
ter of  our  seasons  ceases  there  to  be  recognizable. 

3.  That  the  seasons  always  differ  more  in  proportion  as  we  go 
further  from  the  equator,  and  that,  at  the  same  time,  the  difference 
between  the  summer  and  winter  temperature  becomes  always 
more  considerable. 

4.  That,  even  in  the  neighborhood  of  the  polar  circles,  the 
summer  may  be  very  hot. 

This  we  find  fully  confirmed  by  experience,  notwithstanding 
which,  such  a  consideration  can  only  teach  us  roughly  to  know 
the  distribution  of  heat  upon  the  earth,  it  being  impossible,  from 
the  geographical  latitude  of  a  place,  to  draw  any  conclusion,  even 
remotely  certain,  as  to  its  climatic  relations. 

If  the  whole  earth's  surface  were  covered  by  water,  or  if  it  were 


OBSERVATION   OF   THE   THERMOMETER.  559 

all  formed  of  solid  plane  land,  possessing  everywhere  the  same 
character,  and  having  an  equal  capacity  at  all  places  for  absorb- 
ing and  again  radiating  heat,  the  temperature  of  a  place  would 
depend  only  on  its  geographical  latitude,  and,  consequently,  all 
places  having  the  same  latitude  would  have  a  like  climate.  Now, 
however,  the  action  that  may  be  produced  by  the  solar  rays  is 
modified  by  manifold  causes,  the  climate  of  one  district  depending 
not  only  upon  the  direction  of  the  solar  rays,  but  also  upon  the 
circumstances  under  which  they  act,  such  as  the  conformation  of 
the  land  and  the  sea,  the  direction  and  height  of  the  mountain 
range,  the  direction  of  the  prevailing  wind,  &c.  Hence  it  follows 
that  places  of  the  same  geographical  latitude  have  frequently  a 
very  different  climate,  and  we  may  thus  easily  see  that  theoretical 
considerations  do  not  suffice  as  data,  from  whence  to  draw  conclu- 
sions regarding  climatic  relations ;  the  true  distribution  of  heat 
over  the  earth's  surface  can  only  be  satisfactorily  ascertained  by 
means  of  observations  conducted  for  a  protracted  term  of  years. 
Humboldt  was  the  first  who  entered  here  with  success  upon  the 
course  of  induction,  the  sole  and  only  path  that  leads  to  truth  in 
all  physical  sciences.  On  his  voyages  and  travels  in  both  hemi- 
spheres, he  collected,  with  unwearied  zeal,  facts  which,  by  his 
excellent  mode  of  combining  them,  have  first  laid  the  foundation 
of  scientific  meteorology. 

Observation  of  the  Thermometer. — In  order  to  be  able  to  ob- 
serve accurately  the  temperature  of  the  air  at  different  places,  we 
must  place  a  good  thermometer  in  the  open  air,  upon  the  north 
side  of  a  building,  and  3  or  4  decimetres  removed  from  the  wall, 
so  that  it  may  not  receive  the  sun's  rays ;  we  must,  likewise,  be 
careful  that  there  is  no  white  wall  in  the  neighborhood,  from  which 
rays  of  heat  may  be  reflected  towards  the  thermometer.  If  the 
thermometer  should  be  moistened  by  rain,  we  must  carefully  dry 
the  bulb  five  minutes  before  we  use  it,  for  the  suspended  drops  of 
water  would,  by  their  evaporation,  lower  the  temperature  of  the 
mercury  in  the  bulb. 

It  is  often  of  the  greatest  importance  to  meteorology  to  learn 
the  highest  and  lowest  temperature  that  may  have  prevailed  during 
any  interval,  without  it  being  absolutely  necessary  to  observe  the 
exact  moment  in  which  this  maximum  or  minimum  occurs.  This 
may  be  effected  by  the  thermometrograph,  represented  in  Fig. 


560  OBSERVATION    OF    THE    THERMOMETER. 

517,  which  consists  of  two  thermometers,  the  tubes  of  which  are 
placed  horizontally,  and  of  which  one  is  a  mercurial,  and  the 

Fig.  517. 


other  a  spirit  thermometer.  In  the  tube  of  the  former  lies  a  steel 
pin,  which  is  pushed  through  the  column  of  mercury  when  the 
mercury  in  the  bulb  expands ;  when,  however,  the  thermometer 
is  re-cooled,  the  mercurial  column  recedes,  while  the  steel  pin 
remains  in  the  position  to  which  it  was  pushed  at  the  highest 
stand  of  the  thermometer ;  such  a  thermometer,  consequently, 
yields  the  maximum  of  the  temperature  that  may  have  prevailed 
within  a  certain  period. 

Within  the  tube  of  the  spirit  thermometer,  is  a  very  fine  glass 
rod,  somewhat  thicker  at  its  extremities,  as  may  be  plainly  seen 
in  Fig.  517;  this  glass  rod  lies  within  the  column  of  spirits,  and 
on  the  spirit  cooling  in  the  bulb,  and  the  fluid  retreating  in  the 
tube  to  the  first  knob  of  this  rod,  the  latter  will  be  carried  away 
with  the  retreating  fluid  column,  when  any  further  sinking  of  the 
temperature  occurs,  owing  to  the  adhesion  between  the  spirit  and 
the  glass;  if,  however,  the  fluid  in  the  bulb  be  again  warmed,  it 
will,  on  the  rising  of  the  thermometer,  pass  by  the  rod  without 
carrying  it  with  it;  this  index,  which  must  be  made  of  some  darkly 
stained  glass,  in  order  to  be  made  more  apparent,  remains,  conse- 
quently, lying  in  the  place  corresponding  to  the  minimum  of  the 
temperature  which  prevailed  within  a  certain  period  of  time. 

When  the  bulb  of  the  one  thermometer  lies  on  the  right  side, 
that  of  the  other  is  on  the  left,  and  on  inclining  the  whole  apparatus, 
and  striking  it  gently,  the  steel  rod  will  fall  by  its  weight  on  to 
the  column  of  mercury,  and  the  glass  rod  to  the  very  end  of  the 
column  of  spirit.  If  we  leave  the  apparatus  thus  arranged,  the 
steel  rod  will  be  pushed  on  by  every  ascent  of  the  temperature, 


DIURNAL    VARIATIONS   OF    TEMPERATURE.  561 

while  the  glass  rod  will  be  drawn  back  at  every  depression  of  the 
temperature. 

This  instrument  is  especially  calculated  to  give  the  maximum 
and  minimum  of  the  diurnal  temperature.  On  setting  it  in  the 
proper  manner  every  evening,  we  may,  the  following  evening,  see 
what  has  been  the  highest,  and  what  the  lowest  temperature  dur- 
ing the  last  24  hours. 

Diurnal  Variations  of  Temperature. — In  order  to  be  able  accu- 
rately to  follow  all  the  variations  of  heat  in  the  atmosphere  during 
the  24  hours,  we  must  observe  a  thermometer  at  very  short  inter- 
vals, as,  for  instance,  from  one  hour  to  another.  If  such  obser- 
vations are  to  be  pursued  for  any  length  of  time,  it  is  evident  that 
they  cannot  be  conducted  by  one  single  individual,  but  that  many 
must  combine  for  the  same  purpose  ;  in  every  case  it  is  very  la- 
borious to  institute  a  series  of  observations  of  this  kind. 

From  such  series  of  observations  it  has  been  shown  that  the 
minimum  of  temperature  occurs  shortly  before  sunrise,  and  the 
maximum  a  few  hours  after  12  at  noon,  somewhat  later  in  sum- 
mer, and  somewhat  earlier  in  winter. 

This  course  may  be  easily  explained.  Before  noon,  whilst  the 
sun  is  constantly  rising  higher,  the  earth's  surface  receives  more 
heat  than  it  radiates ;  its  temperature  and  that  of  the  atmosphere 
must,  therefore,  increase ;  this  continues  somewhat  beyond  noon ; 
but  as  the  sun  sinks  lower,  and  its  rays  become  less  effective,  the 
heated  earth  radiates  more  heat  than  can  be  supplied  by  the  solar 
rays;  this  cooling  naturally  continues  after  sunset,  until  the 
morning-dawn  announces  the  return  of  the  sun. 

The  diurnal  variations  in  the  thermometer  do  not  always  follow 
this  normal  course,  which  may  frequently  be  disturbed  by  foreign 
influences,  as,  for  instance,  changes  of  weather,  &c. ;  in  order, 
therefore,  to  ascertain  with  exactitude  the  law  of  diurnal  varia- 
tions of  heat,  we  must  deduce  the  mean  normal  course  from  a 
combination  of  as  many  numerous  observations  as  can  possibly 
be  instituted. 

By  taking  the  mean  of  every  24  hours'  observations,  we  obtain 

the  mean  temperature  of  the  day. 

As  it  is  uncommonly  wearisome  and  laborious  to  pursue  for  any 
length  of  time  these  hourly  observations  of  the  thermometer,  it  is 
of  the  greatest  importance  to  meteorology  to  devise  methods  by 


562  MEAN    TEMPERATURE    OF    THE   MONTHS. 

which  the  mean  diurnal  temperature  may  be  ascertained  without 
making  these  hourly  observations.  Twice  in  the  day  the  ther- 
mometer must  indicate  the  mean  diurnal  temperature ;  it,  there- 
fore, seems  the  simplest  to  calculate  the  hours  in  which  such  is 
the  case,  and  then  limit  our  observations  of  the  thermometer  to 
those  periods  of  the  day ;  such  a  course  may,  however,  easily 
lead  us  into  errors,  since  the  thermometer  varies  most  suddenly 
exactly  at  this  time,  and  we  should  thus  commit  a  very  considera- 
ble mistake  in  our  calculations,  if  our  observations  were  made 
either  a  little  too  early  or  too  late.  A  far  more  correct  result  is 
obtained  by  observing  the  thermometer  at  several  similar  hours, 
for  instance,  at  4  and  10  A.M.,  and  at  4  and  10  P.M.  ;  this  method 
is,  as  Brewster  has  shown,  correct  to  TVth  of  a  degree ;  we  like- 
wise obtain  a  very  useful  result  by  making  our  observations  at  7 
A.M.  at  noon,  and  at  10  P.M.,  and  then  taking  the  mean  of  these 
three  periods. 

The  mean  of  the  highest  and  lowest  degree  of  the  thermometer 
during  the  24  hours  varies  so  inconsiderably  from  the  actual  mean 
temperature  derived  from  hourly  observations,  that  we  may  more 
easily  compute  the  mean  diurnal  temperature  by  aid  of  the  ther- 
mometrograph  described  at  page  560. 

Mean  Temperature  of  the  Months,  and  of  the  Year. — When  we 
know  the  mean  temperature  of  all  the  days  of  a  month,  we  have 
only  to  divide  the  sum  of  the  mean  diurnal  temperatures  by  the 
number  of  days,  in  order  to  obtain  the  mean  temperature  of  the 
month. 

On  taking  the  arithmetical  mean  from  the  mean  temperature 
found  for  the  12  months  of  the  year,  we  obtain  the  mean  tempera- 
ture of  the  year. 

In  order  to  determine,  with  exactness,  the  mean  temperature  of 
a  place,  we  must  take  the  mean  of  the  mean  temperatures  obtained 
from  a  large  series  of  calculations.  In  general,  the  mean  annual 
temperatures  do  not  vary  much,  so  that  we  obtain  the  mean  tem- 
perature of  a  place  with  tolerable  accuracy,  even  when  we  only 
know  it  for  a  few  years.  For  Paris,  the  mean  temperatures  of  the 
years  intervening  between  1803  and  1816,  were  as  follows : 

51°  50,8°  49,6° 

52  51,1  49,4 


MEAN    TEMPERATURE    OF    THE    YEAR.  563 

49,2°  51°  51° 

53,3  51  49,2 

51,3  49,6 

The  highest  of  these  mean  annual  temperatures  varies  only 
about  4,1°  from  the  lowest.  On  taking  the  mean  of  these  14 
numbers,  we  obtain  as  a  mean  temperature  for  Paris  50,6°,  whilst 
the  amount  derived  from  a  series  of  30  annual  mean  temperatures 
is  51,4°. 

In  order  to  find  the  true  mean  temperature  of  a  month,  we 
must  know  the  mean  temperature  of  this  month  for  a  series  of 
years,  and  take  the  mean  of  these. 

The  greatest  heat  generally  occurs  in  our  latitudes  some  time 
after  the  summer  solstice,  and  the  greatest  cold  some  time  after 
the  winter  solstice. 

July  is,  on  an  average,  the  hottest,  and  January  the  coldest 
month.  If  the  period  of  the  highest  and  lowest  temperature  is 
not  exactly  the  same  for  all  places  of  the  same  hemisphere,  the 
difference  is  only  occasioned  by  local  influences. 

We  may,  on  an  average,  consider  the  26th  of  July  as  the 
hottest,  and  the  14th  of  January  as  the  coldest  day  of  the  year 
for  the  temperate  zone  of  the  northern  hemisphere. 

It  has  been  proved  from  numerous  observations  on  temperature, 
that  the  mean  annual  temperature  generally  occurs  on  the  24th  of 
April,  and  the  21st  of  October  in  the  northern  temperate  zone ; 
the  annual  course  of  the  heat  in  these  parts  is  therefore  as  follows. 
The  temperature  rises  from  the  middle  of  January  at  first  slowly, 
more  rapidly  in  April  and  May,  and  again  more  slowly  until  the 
middle  of  July,  from  which  period  it  diminishes  but  slowly  in 
August,  more  rapidly  in  September  and  October,  finally  reaching 
its  minimum  again  in  the  middle  of  January.  This  admits  of  an 
easy  explanation.  When  the  sun,  after  the  winter  solstice,  again 
ascends,  this  ascent  goes  on  so  slowly,  and  the  days  increase  so 
little,  that  as  yet  no  more  powerful  effect  from  the  sun's  rays  is 
possible.  On  this  account,  the  minimum  of  the  yearly  temperature 
occurs  after  the  winter  solstice  ;  a  rise  of  temperature  first  takes 
place  when  the  sun  has  returned  somewhat  farther  north.  About 
the  time  of  the  equinoxes,  the  sun's  progress  in  the  heavens  to- 


564  MEAN    TEMPERATURE    OF    THE    YEAR. 

wards  the  north  is  quickest:  the  increase  of  temperature  for  this 
reason  is  at  this  time  the  most  perceptible. 

When  the  sun  has  attained  its  highest  position,  the  earth  has 
not  yet  become  so  warmed  that  the  heat  which  the  ground  loses 
by  radiation  is  equal  to  the  quantity  of  heat,  which  it  receives 
from  the  sun's  rays;  the  balance  would  only  be  restored  after  the 
sun  had  remained  a  longer  time  at  its  northern  solstice.  But  now 
the  sun  goes  back  after  its  summer  solstice,  very  slowly  at  first. 
The  effect  of  the  sun's  rays  is  for  some  time  quite  as  powerful  as 
at  the  moment  of  the  solstice ;  the  temperature,  therefore,  will 
still  rise  after  the  longest  day,  and  indeed  even  to  the  middle  of 
July,  and  then  again  fall.  These  considerations  lead  to  the  divi- 
sion of  the  year  into  four  seasons. 

The  astronomical  division,  when  the  seasons  are  limited  by 
the  equinoxes  and  solstices,  is  the  most  suitable  to  meteorology. 
It  would  be  better  were  we  to  divide  the  year  in  such  a  manner, 
that  the  hottest  month  (July)  should  fall  in  the  middle  of  summer, 
and  the  coldest  month  (January)  in  the  middle  of  winter.  Ac- 
cording to  this,  winter  would  include  the  months  of  December, 
January,  and  February;  spring,  March,  April,  and  May;  summer, 
June,  July,  and  August;  and  autumn,  September,  October,  and 
November.  According  to  this  signification,  we  must  understand 
the  seasons  given  in  the  following  table,  which  contains  the  mean 
annual  temperature,  mean  temperature  of  individual  years,  and 
the  hottest  and  coldest  months  for  a  large  number  of  places  scat- 
tered over  different  parts  of  the  earth's  surface. 

The  numbers  of  this  table  are  only  mean  numbers,  from  which 
the  true  temperature  inclines  sometimes  towards  one  side,  some- 
times towards  the  other,  and  thus,  too,  the  mean  temperatures  of 
the  hottest  and  coldest  months  by  no  means  indicate  the  limits 
between  which  the  thermometer  may  fluctuate  at  one  and  the  same 
spot.  It  thus  happens,  that  even  in  districts  enjoying  a  warm 
climate  and  a  mild  winter,  an  extraordinary  degree  of  cold  is 
often  felt;  thus,  for  instance,  in  the  year  1507  the  harbor  of  Mar- 
seilles was  frozen  over  its  whole  extent,  for  which  a  cold  of  at 
least  —  0,4°  was  requisite;  in  the  year  1658,  Charles  X.,  with 
his  whole  army  and  their  heavy  artillery,  crossed  the  little  Belt. 
In  1709  the  Gulf  of  Venice,  and  the  harbors  of  Marseilles,  Genoa, 
and  Cette  were  frozen  over;  and  in  1789  the  thermometer  fell  at 


MEAN    TEMPERATURE    OF    FORTY-THREE   PLACES. 


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566  MEAN    TEMPERATURE    AT    DIFFERENT    PLACES. 

Marseilles  to  —  16°.     The  following  table  gives  the  highest  and 
lowest  degrees  of  temperature  observed  at  different  places. 

Minimum.     Maximum.    Difference. 

Surinam         ....     70,3°         90,1°  19,8° 

Pondicherry  .         .         .         .71  112,3  41,3 

Esna  (Egypt)         .         .         .  117,3 

Cairo  ....     48,3  104,2  55,9 

Rome  ....     22,1  100,4  78,3 

Paris  .         .         .         —    9,3  101,1  110,4 

Prague  .         .         .         —17,5  95,9  113,4 

Moscow         .         .         .         —  38  89,6  127,6 

Fort  Reliance  (North  America)  —  70 

Considerable  deviations  from  the  normal  annual  course  of  heat 
do  not  occur  locally,  but  are  scattered  over  wide  districts;  thus, 
for  instance,  the  winter  of  1821  and  1822  was  very  mild  in  Europe, 
but  in  the  December  of  the  latter  year  a  severe  cold  prevailed 
over  the  whole  of  Western  Europe.  A  similar  very  considerable 
deviation  never  has,  however,  been  spread  over  an  entire  hemi- 
sphere. The  northern  hemisphere  is  generally  divided  in  a 
northern  to  a  southern  direction  into  two  halves,  upon  which  op- 
posite deviations  from  the  normal  temperature  may  be  observed; 
these  deviations  are  greatest  in  the  middle  of  the  two  halves, 
while  a  more  average  temperature  is  perceived  where  they  ap- 
proach each  other. 

Thus,  in  February,  1828,  it  was  very  cold  in  Kasan  and 
Irkutzk,  unusually  mild  in  North  America,  whilst  Europe  remained 
unaffected  between  these  two  opposite  deviations.  In  December, 
1829,  this  maximum  of  cold  inclined  towards  Berlin,  while  it 
also  continued  to  be  very  marked  at  Kasan;  in  North  America, 
however,  the  weather  was  unusually  mild ;  but  in  December,  1831, 
the  excessive  cold  was  limited  to  America.  Generally  speaking, 
these  deviations  from  the  average  range  of  heat  are  observed  to 
be  similar  in  Europe  and  Asia,  and  opposite  in  America. 

Frequently,  although  not  so  remarkable,  the  boundary  line  of 
opposite  deviations  runs  from  east  to  west. 

A  deviation  from  the  mean  temperature  often  continues  for  a 
long  time  in  the  same  direction.  Thus,  from  June,  1815,  to  the 
December  of  1816,  there  prevailed  in  Europe  an  unusually  low 
degree  of  temperature,  which  occasioned  the  failures  in  the  crops 


ISOTHERMAL    LINES.  567 

in  1816 ;  1822  was  a  remarkable  year  for  the  vines,  the  unusual 
heat  continuing  then  from  November,  1821,  to  November,  1822. 

From  this  it  follows,  that  the  opinion  so  prevalent  of  a  cold 
winter  succeeding  a  hot  summer,  and  a  warm  winter  a  cold  sum- 
mer, is  altogether  erroneous,  since  the  contrary  often  occurs,  as 
may  be  seen  from  the  examples  above  given ;  thus,  too,  the  hot 
summer  of  1834  succeeded  a  very  mild  winter. 

These  deviations  from  the  mean  range  of  heat  are  more  marked 
in  winter  than  in  summer. 

From  all  this  it  appears  highly  probable  that  the  same  quantity 
of  heat  is  always  distributed  over  the  earth's  surface,  although 
unequally.  A  cold  winter  is  the  consequence  of  a  long  preva- 
lence of  north-east  winds,  and  a  cold  summer  is  induced  by  the 
continuance  of  south-west  winds;  these  alternating  exclusively 
prevalent  currents  of  air  being,  as  Dove  has  shown,  the  controlling 
agents  in  the  relations  of  weather.  If  a  hot  summer  is  to  succeed 
a  cold  winter,  the  north-east  wind  must  prevail  throughout  the 
whole  year ;  while,  on  the  other  hand,  the  wind  must  blow  chiefly 
from  the  south-west  for  the  same  space  of  time  to  bring  a  cold 
summer  after  a  mild  winter. 

Isothermal  Lines. — A  table  of  the  kind  given  at  page  565,  con- 
tains many  of  the  elements,  from  which  we  may  calculate  the 
distribution  of  heat  over  the  earth's  surface.  At  all  events,  we 
may  see  from  such  a  table  that  all  places  lying  under  the  same 
degree. of  latitude  have  not  the  same  mean  temperature.  Thus, 
for  instance,  the  mean  annual  heat  at  the  North  Cape  is  32,1° ; 
whilst  Nain,  on  the  coast  of  Labrador,  has  a  mean  annual  tem- 
perature of  25°,  although  Labrador  is  14°  south  of  the  North 
Cape.  Humboldt  was  the  first  to  give  us  a  clear  view  of  the 
distribution  of  heat  over  the  earth,  making  use,  for  this  purpose, 
of  his  isothermal  lines,  by  which  he  connected  together  all  such 
places  in  the  same  hemisphere  having  equal  mean  annual  tempe- 
ratures. 

If  we  suppose,  for  instance,  a  traveler  starting  from  Paris  to 
make  a  journey  round  the  earth  in  such  a  manner  as  to  visit  all 
places  of  the  northern  hemispheres  which  have  the  same  mean 
annual  heat  as  Paris,  that  is,  51,4°,  the  course  he  will  thus  pursue 
will  be  a  line  of  equal  mean  annual  heat,  consequently  an  isother- 
mal line;  this  line,  instead  of  corresponding  with  the  degree  of 


568  ISOTHERMAL    LINES. 

latitude  of  Paris,  will  be  irregular  and  curved,  passing  through 
places  having  a  very  different  latitude  from  Paris. 

Fig.  518  represents  the  earth's  surface  in  Mercator's  propor- 
tions, with  the  isothermal  lines  at  every  5  degrees.  At  the  ter- 
restrial equator,  the  mean  temperature  of  the  sea-coast  is  81,5°, 
although  somewhat  less  upon  the  western  coast  of  America  and 
Africa ;  in  the  interior  of  these  two  continents,  especially  in  that 
of  Africa,  the  mean  temperature  is  higher  than  on  the  sea-shore ; 
the  mean  temperature  of  the  equator  in  the  latter  continent  is 
above  84°. 

An  examination  of  the  chart  in  Fig.  518,  will  spare  us  a  fur- 
ther description  of  the  course  of  the  isothermal  lines.  We  observe 
how  considerable  their  curves  become  in  the  northern  hemisphere 
the  further  we  remove  from  the  equator;  the  isothermal  line  of 
32°,  for  instance,  ascends  from  the  southern  end  of  the  coast  of 
Labrador  across  Iceland  towards  the  North  Cape,  in  order  to  de- 
cline again  considerably  in  the  interior  of  Asia. 

Where  the  isothermal  lines  incline  the  farthest  towards  the 
south,  they  describe  a  concave ;  and  where  they  ascend  the  highest 
towards  the  north,  a  convex  vertex.  The  southern  turning  points 
of  the  isothermal  lines  lie  in  the  east  of  North  America  and  in  the 
interior  of  Asia,  while  the  northern  turning  points  lie  on  the 
western  coasts  of  Europe  and  America. 

The  relations  of  temperature  of  the  southern  hemisphere  are  not 
nearly  so  perfectly  known  to  us  as  those  of  the  northern  hemi- 
sphere; we  may,  however,  consider  it  as  established,  that  the 
southern  is  colder  than  the  northern  hemisphere,  although  the 
difference  may,  perhaps,  be  less  considerable  than  we  are  gene- 
rally disposed  to  assume  it.  The  circumstance  that  has  probably 
contributed  to  the  opinion  that  the  southern  is  so  much  colder 
than  the  northern  hemisphere,  is,  that  the  relations  of  temperature 
of  the  southern  part  of  America  have  been  compared  with  those 
of  like  northern  latitudes  in  Europe,  where  the  isothermal  lines 
ascend  so  very  considerably  to  the  north;  the  matter  is  very 
different  when  we  compare  districts  of  South  America  with  those 
lying  equally  far  from  the  equator  on  the  east  side  of  North 
America. 

That  the  southern  hemisphere  is  somewhat  colder  than  the 
northern,  arises  probably  from  the  fact,  that  in  the  former,  water, 
and  in  the  latter,  land,  predominates.  The  continent  is  much  more 


ISOTHERMAL    LINES. 


.069 


48' 


570  ISOTHERMAL    AND    ISOCHIMENAL    LINES. 

heated  by  the  absorption  of  the  sun's  rays  than  the  sea,  which 
reflects  a  great  portion  of  them. 

Isothermal  and  Isochimenal  Lines. — We  have  thus  stated  that 
all  places  lying  on  the  same  parallel  circle  have  not  the  same 
climate;  here, however,  the  question  arises,  whether  all  places  on 
the  same  isothermal  lines,  consequently  such  as  have  the  same 
mean  annual  heat,  have  likewise  otherwise  equal  climatic  rela- 
tions. We  need  only  look  at  the  table,  page  565,  in  order  to 
convince  ourselves  that  such  is  not  the  case.  Thus,  for  instance, 
Edinburgh  and  Tubingen  have  the  same  mean  annual  temperature 
of  47,6°;  at  the  former  place,  however,  the  mean  temperature  of 
winter  is  38,6°,  at  the  latter  32,2°  F.;  Tubingen,  consequently, 
has  a  far  colder  winter  than  Edinburgh.  But  then,  again,  the 
mean  summer  temperature  of  Tubingen  is  62,7°  F.,  while  it  is 
only  58,4°  F.  for  Edinburgh.  With  a  like  mean  annual  tempe- 
rature, Edinburgh  has,  therefore,  a  milder  winter  and  a  colder 
summer  than  Tubingen. 

In  order  to  know  the  relations  of  heat  of  a  country,  it  is  not 
sufficient  to  be  acquainted  with  its  mean  annual  temperature;  we 
must  also  know  how  heat  is  distributed  during  the  different 
seasons  of  the  year.  This  distribution  may  be  shown  upon  an 
isothermal  chart,  by  setting  down,  according  to  Humboldfs  idea, 
the  mean  summer  and  winter  temperature  against  the  different 
places  upon  one  and  the  same  isothermal  line,  which  could  not  be 
done  on  our  isothermal  chart,  owing  to  its  small  size ;  we  shall 
thus  see,  that  in  the  immediate  vicinity  of  the  convex  summit  of 
the  isothermal  lines,  the  differences  between  the  mean  summer  and 
winter  temperature  are  the  least;  the  same  reasons,  consequently, 
which  cause  the  isothermal  lines  upon  the  western  coast  of  Europe 
and  America  to  rise  so  far  to  the  northward,  make  the  difference 
between  the  summer  and  winter  temperature  less  considerable. 
A  very  good  idea  of  the  distribution  of  heat  in  winter  and  summer 
may  be  obtained  by  means  of  a  chart,  in  which  all  places  having 
the  same  mean  winter  temperature  are  connected  together  by 
curved  lines,  as  are  also  all  the  places  that  have  the  same  mean 
summer  temperature.  The  lines  of  like  mean  winter  temperature 
are  termed  isochimenal,  and  those  of  like  mean  summer  tempe- 
rature, isothermal.  Fig.  519  represents  a  small  chart  of  Europe 
with  the  isothermal  and  isochimenal  lines  drawn  at  every  5 
degrees. 


ISOTHERMAL   AND    ISOCHIMENAL    LINES. 


571 


Fig.  519. 


flOC 


— 20  C.  +4    F. 


The  curves,  whose  corresponding  temperatures  are  on  the  right 
the  chart,  are  the  isockimenal,  and  the  other  the  isothermal 
«.     We  may  easily  see  from  this  chart,  that  the  western  coasts 
the  southern  part  of  Norway,  Denmark,  a  portion  of  Bohemia 
Hungary,  Transylvania,  Bessarabia,  and  the  southern  extre- 
mity of  the  peninsula  of  the  Crimea,  have  the  same  mean  winter 
temperature  of  0-  (32°  F.).     Bohemia,  however,  has  the  same 
immer  heat  as  the  districts  lying  at  the  mouth  of  the  Garonne, 
in  the  Crimea  the  summer  is  far  hotter.     Dublin  has  the 
ame  mean  winter  temperature,  viz.,  5°  (41°  F.)  as  Nantes,  Upper 
Italy,  and  Constantinople,  with  the  same  summer  heat  as  Dron- 
theim  and  Finland. 

The  isothermal  line  of  20°  (68°  F.)  passes  from  the  mouth  of  the 
Garonne,  nearly  over  Strasburg  and  Wurzburg  to  Bohemia,  the 
Ukraine,  the  country  of  the  Don  Cossacks,  somewhat  to  the  north 
of  the  Caspian  Sea ;  how  different,  however,  is  the  mean  winter 
temperature  at  different  places  upon  this  line !  On  the  western 
coasts  of  France  it  is  5=  '41-  F.),  in  Bohemia  0°  (32°  F.),  in  the 
Ukraine  — 5C  (23°  F.),  and  somewhat  to  the  north  of  the  Caspian 
Sea  even  — 10°  (14°  F.). 


572  THE    CLIMATE    ON    LAND    AND    AT    SEA. 

The  Climate  on  Land  and  at  Sea.  —  The  consideration  of  the  last 
map,  and  the  table  at  page  565,  leads  us  to  the  important  differ- 
ence between  the  climate  at  sea  and  on  the  land,  or,  as  we  may 
also  express  it,  between  the  continental  and  littoral  climate.  The 
differences  between  the  summer  and  winter  temperature  increase 
with  the  distance  from  the  sea  ;  on  the  sea-side  the  summers  are 
cool  and  the  winters  mild,  whilst  in  the  interior  we  have  hot  sum- 
mers and  cold  winters.  These  differences  appear  very  marked, 
on  comparing  the  relations  of  temperature  of  the  western  shores  of 
Europe  with  those  of  northern  Asia.  In  order  to  be  able  easily 
to  mark  the  relation  of  the  mean  annual  temperature  to  the  dis- 
tribution of  heat,  we  have  given  examples  derived  from  the  table, 
page  565,  the  mean  annual  temperature  first,  the  mean  summer 
temperature  above,  and  the  mean  winter  temperature  below  a 
horizontal  line  : 

Littoral  climate.  Continental  climate. 

NOTthCape    .    -OiM 


Mh*.    .     ,0^(3^1)     ***.     .-  0, 

M05COW    ._3,a 

The  influence  that  such  climatic  differences  must  exercise  upon 
vegetation  is  evident.  Thus,  in  many  parts  of  Siberia,  at  Jakuzk, 
for  instance,  where  the  mean  annual  temperature  is  -  -  9,70 
(14,7°  F.),  while  the  mean  winter  temperature  is  —38,9°  (38,1°), 
wheat  and  rye  are  raised  upon  a  soil  which  remains  constantly 
frozen  at  the  depth  of  3  feet;  while  in  Iceland,  where  the  mean 
temperature  of  the  year  is  very  much  higher,  and  the  winter's 
cold  but  inconsiderable,  it  is  impossible  to  raise  any  of  the 
cereals,  as  the  low  summer  temperature  does  not  suffer  them  to 
ripen. 

In  the  north-east  of  Ireland,  where  there  is  scarcely  any  ice  or 
frost  in  the  winter,  at  the  same  latitude  as  Konigsberg,  the  myrtle 
thrives  as  well  as  in  Portugal;  on  the  coast  of  Devonshire,  the 
Camellia  Japonica  and  the  Fuchsia  Coccinea  live  through  the 
winter  in  the  open  air  ;  the  winter  is  not  colder  in  Plymouth 
than  in  Florence  and  Montpellier;  the  vine  will  not  thrive  in 
England,  however,  for,  although  it  can  endure  a  tolerably  strong 
degree  of  cold,  it  requires  a  hot  summer  to  make  the  fruit  ripen 
and  yield  a  drinkable  wine. 


CAUSES    OF    CURVATURE   OF    THE    ISOTHERMAL    LINES.    573 

These  differences  are  owing  to  the  more  easy  absorption  and 
radiation  of  heat,  which  becomes  heated  and  again  cooled  more 
rapidly  than  the  sea,  which,  by  the  continent,  is  everywhere  of 
a  uniform  nature,  and  from  its  transparency,  and  the  considera- 
ble amount  of  specific  heat  of  water,  is  neither  so  rapidly  heated, 
nor  so  speedily  deprived  of  the  heat  it  has  once  acquired.  The 
temperature  of  the  surface  of  the  sea  is,  on  that  account,  far  more 
uniform ;  the  diurnal  as  well  as  the  annual  alternations  are  incom- 
parably less  than  in  the  middle  of  large  continents,  whence  arises 
the  above-mentioned  difference  between  the  climate  on  the  land 
and  at  sea  ;  it  is,  likewise,  augmented  by  the  sky,  which  is  mostly 
overcast  on  the  shores  of  countries  lying  towards  the  north,  and 
tempers  the  heating  influence  of  the  solar  rays  in  summer,  and 
checks  the  excessive  cooling  of  the  earth  in  winter  by  radiation 
of  heat. 

Causes  of  the  Curvature  of  the  Isothermal  Lines. — The  most 
important  causes  that  contribute  to  the  curvature  of  the  isother- 
mal lines  so  much  to  the  north  on  the  western  shores  of  Europe 
and  America,  are  essentially  as  follows: 

In  the  northern  temperate  zone,  south-west  and  north-east 
winds  prevail.  The  former  come  from  the  equatorial  districts, 
and  partially  bear  the  heat  of  the  tropics  towards  colder  regions ; 
this  warming  influence  of  the  south-west  winds  is,  however, 
most  marked  in  those  districts  which  are  the  most  exposed  to 
south-western  currents  of  air,  and  thus  we  see  why  it  is  that  the 
western  shores  of  great  continents  become  warmer  than  the  eastern 
coasts,  and  that  the  isothermal  lines  in  Europe,  which  is  actually 
only  a  peninsular  prolongation  of  the  Asiatic  continent,  and  on  the 
western  shores  of  North  America,  ascend  further  to  the  north 
than  in  the  interior  of  Asia,  and  on  the  eastern  shores  of  North 
America. 

A  second  cause,  to  which  Europe  owes  its  relatively  warm  cli- 
mate, is  this,  that,  in  the  equatorial  region,  it  is  bounded  towards 
the  south,  not  by  a  sea,  but  by  an  extensive  continent,  Africa, 
whose  vast  extent  of  desert  and  sand  render  it  extremely  hot  when 
exposed  to  the  vertical  solar  rays.  A  warm  current  of  air  rises 
continually  from  the  glowing  hot  sandy  wastes,  to  descend  again 
in  Europe. 

Finally,  the  current  known  by  the  name  of  the  Gulf  Stream, 
contributes  considerably  to  make  the  European  climate  milder. 


574    CAUSES    OF    CURVATURE    OF    THE    ISOTHERMAL    LINES. 

The  origin  of  this  current  is  to  be  sought  for  in  the  Gulf  of 
Mexico,  where  the  water  is  at  a  temperature  of  87°  F.  Issuing 
from  the  Gulf,  between  Cuba  and  Florida,  the  stream  at  first  skirts 
the  American  shores,  and  then,  as  it  comes  into  higher  latitudes, 
turns  with  decreasing  temperature  eastward  towards  Europe. 
Although  the  Gulf  Stream  does  not  actually  reach  the  shores  of 
Europe,  it  nevertheless  distributes  its  heated  waters,  under  the 
influence  of  the  prevailing  south-west  winds,  to  the  European 
waters,  as  is  proved  by  our  finding,  on  the  western  shores  of  Ire- 
land and  on  the  coast  of  Norway,  the  fruits  of  trees  that  grow  in 
the  hot  zone  of  America;  the  west  and  south  winds  remain,  there- 
fore, long  in  contact  with  a  sea-water,  whose  temperature  between 
45  and  50  degrees  of  latitude  does  not,  even  in  January,  sink 
below  from  51°  to  48°  F.  Northern  Europe  is  thus  separated  by 
the  influence  of  the  Gulf  Stream  from  the  circle  of  polar  ice,  by 
means  of  a  sea  free  from  ice ;  even  at  the  coldest  season  of  the 
year  the  limits  of  polar  ice  do  not  reach  the  European  shores. 

Whilst  all  circumstances  thus  combine  to  raise  the  temperature 
in  Europe,  many  causes  contribute  in  Northern  Asia  to  lower  the 
isothermal  lines  very  considerably.  In  the  south  of  Asia  there 
are  no  extensive  districts  of  land  between  the  tropics,  but  merely 
a  few  peninsulas  comprised  within  this  zone ;  the  sea,  however, 
does  not  become  so  much  heated  as  the  African  deserts,  partly 
because  the  water  absorbs  rays  of  heat  to  an  incomparably  smaller 
extent,  and  partly,  also,  because  a  great  quantity  of  heat  goes  off 
in  the  latent  state,  owing  to  the  constant  evaporation  of  water 
from  the  surface  of  the  sea.  The  warm  currents  of  air,  which, 
rising  from  the  basin  of  the  Indian  Ocean,  would  convey  the 
heat  of  the  tropics  to  the  interior  and  north  of  Asia,  are  impeded 
in  their  course  by  the  huge  mountain  ranges  in  the  south  of  Asia, 
whilst  the  land,  which  gradually  flattens  towards  the  north,  is  left 
exposed  to  the  north  and  north-east  winds.  While  Europe  does 
not  stretch  far  northward,  Asia  penetrates  a  considerable  way  into 
the  Arctic  Sea,  which,  deprived  of  all  those  heating  influences  by 
which  the  temperature  of  the  European  seas  is  raised,  is  almost 
always  covered  with  ice.  In  every  direction  the  northern  shores 
of  Asia  penetrate  the  wintry  limits  of  the  polar  ice,  the  summer 
boundary  of  which  is  only  removed  for  a  short  time,  and  at  a  few 
places  from  the  coasts;  that  this  circumstance,  however,  must 
considerably  lower  the  temperature,  will  be  easily  understood 


TEMPERATURE  OF  THE  GROUND.  575 

when  we  consider  how  much  heat  becomes  latent  by  the  fusion 
of  such  masses  of  ice. 

The  considerable  depression  of  the  isothermal  lines  in  the  in- 
terior, and  upon  the  eastern  shores  of  North  America,  depends  in 
part  upon  the  south-west  winds,  which,  not  being  sea,  but  land- 
winds,  are  therefore  unable  any  longer  to  diffuse  the  milder  influ- 
ence that  they  exert  upon  the  western  shores.  Whilst  the  European 
shores  are  washed  by  warmer  waters,  cold  sea-currents  come 
from  the  north  and  south  towards  the  eastern  shores  of  North 
America.  Such  a  current  coming  from  Spitzbergen,  passes  be- 
tween Iceland  and  Greenland,  and  then  combines  with  the 
currents  that  come  from  Hudson's  Bay  and  Baffin's  Bay,  passes 
down  the  coast  of  Labrador,  past  Newfoundland,  and  empties 
itself  finally  in  the  Gulf  Stream  at  44°  N.  lat.  This  arctic  cur- 
rent bears  the  cold  of  the  polar  regions,  partly  by  the  low  tem- 
perature of  the  water,  but  chiefly  by  floating  icebergs,  into  the 
southern  districts,  and  thus  becomes  a  main  cause  of  the  con- 
siderable depression  of  the  isothermal  lines  on  the  eastern  coasts 
of  America. 

Temperature  of  the  Ground. — We  have  hitherto  only  spoken  of 
the  temperature  of  the  air,  and  not  of  that  of  the  upper  layers  of 
the  ground,  which  vary  considerably  from  the  temperature  of  the 
air,  according  to  the  nature  of  the  surface.  Where  the  soil  is 
barren,  deprived  of  vegetable  growths,  stony  or  sandy,  it  becomes 
far  hotter  by  the  absorption  of  rays  of  heat  than  one  that  is 
covered  with  plants;  for  instance,  a  piece  of  meadow-land  be- 
comes much  cooler  by  nocturnal  radiation  than  the  air,  whose 
temperature  is  made  more  uniform  by  the  effect  of  continued 
currents.  In  the  deserts  of  Africa,  the  heat  of  the  sand  often 
amounts  to  from  122°  to  140°  F.  A  soil  covered  with  vegetable 
growths  remains  cooler,  owing  to  the  solar  rays  not  striking  it 
directly ;  the  plants  themselves  combine,  to  a  certain  degree,  a 
large  amount  of  heat,  whilst  a  quantity  of  water  is  evaporated  by 
vegetation  ;  but  they  cool  so  considerably  in  their  great  capacity 
of  emission  of  heat  by  radiation,  as  we  shall  see  when  we  come 
to  speak  of  the  formation  of  dew,  that  the  temperature  of  the 
grass  often  falls  from  10  to  15°  below  that  of  the  air.  In  the 
interior  of  woods  and  forests  the  air  is  constantly  cool,  owing  to 
the  thick  leafy  covering  acting  in  the  same  cooling  manner  as  the 


576  TEMPERATURE  OF  THE  GROUND. 

covering  of  grass,  and  because  the  cooled  air  is  precipitated  upon 
the  tops  of  the  trees. 

The  heat  on  the  uppermost  surface  of  the  ground  can  only 
penetrate  to  the  interior  by  degrees,  owing  to  its  imperfect  capa- 
city for  conducting  heat ;  the  deeper  layers  of  the  soil  lose  their 
heat  less  rapidly  than  the  upper  ones,  and  thus  at  some  little 
depth  the  variations  of  temperature  are  less  marked  than  on  the 
surface  itself.  In  Germany  these  variations  of  temperature  dis- 
appear at  a  depth  of  6  decimetres,  (about  190  feet,)  and  at  a 
greater  depth  the  annual  variations  even  vanish ;  so  that  a  tem- 
perature prevails  here  differing  but  little  from  the  mean  tempera- 
ture of  the  place. 

Although  all  the  heat  upon  the  earth's  surface  comes  from  the 
sun  alone,  the  earth  has  also  its  own  peculiar  heat,  as  may  be 
proved  by  the  increase  of  temperature  observed  at  great  depths. 
If  the  heat  augment  towards  the  centre  of  the  earth  in  the  same 
proportion  as  our  observations  indicate,  at  the  depth  of  3200 
metres,  there  would  be  a  temperature  equal  to  that  of  boiling 
water,  while  at  the  centre  of  the  earth  all  bodies  would  be  in  a 
state  of  fusion.  That  upon  the  surface  of  our  planet  we  perceive 
nothing  of  this  intense  heat  of  its  interior  may  be  explained  by  the 
bad  capacity  for  conducting  heat  possessed  by  the  cooled  earth's 
crust,  which  surrounds  this  glowing  nucleus. 

Springs  that  yield  the  most  copious  supply  of  water  vary  but 
little  in  their  temperature  at  the  different  seasons ;  in  our  hemi- 
sphere they  attain  their  highest  temperature  in  September,  and 
their  lowest  in  March ;  the  difference  between  the  two  amounting 
generally  to  only  1  or  2°. 

Springs  which  arise  from  a  great  depth  have  a  far  higher  tem- 
perature, as  is  the  case  with  salt  and  other  mineral  springs.  The 
water  of  many  of  these  salt  springs  has  almost  the  temperature 
of  the  boiling  point. 

Decrease  of  Temperature  in  the  Upper  Regions  of  the  Mr. — 
The  heating  of  the  air  arises  from  two  causes :  in  the  first  place 
it  absorbs  a  part  of  the  rays  of  heat  coming  from  the  sun ;  but  as 
the  air  absorbs  rays  of  heat  to  a  much  more  inconsiderable  degree 
than  the  earth's  surface,  the  air  is  likewise  much  less  heated  by 
the  absorption  of  rays  of  heat  than  the  ground ;  thus  the  atmo- 
sphere receives  the  greatest  portion  of  its  heat  from  below. 

If  the  air  were  not  an  elastic  fluid,  the  density  of  the  atmosphere 


TEMPERATURE  OF  THE  GROUND.          577 

would  remain  the  same  for  all  elevations;  the  strata  of  air  warmed 
upon  the  surface  would  ascend  to  the  limits  of  the  atmosphere, 
and  the  uppermost  strata  of  the  air  surrounding  our  earth  would 
likewise  be  the  warmest.  But  as  the  warm  strata  of  air  expand 
in  their  ascent,  heat  is  absorbed  by  this  expansion,  and  their  tem- 
perature lowered :  from  which  it  follows  that  the  higher  strata  are 
the  coldest. 

We  may  easily  convince  ourselves  that  such  a  depression  of 
temperature  actually  occurs  in  the  higher  regions  of  the  air,  when 
we  ascend  into  these  regions  by  means  of  a  balloon,  or  to  the 
summit  of  some  high  mountain. 

In  the  Alps,  an  elevation  of  585  feet  corresponds,  on  an  average, 
to  a  depression  of  temperature  of  1°. 

As  a  consequence  of  the  decrease  of  temperature  with  an 
increase  of  altitude,  the  summits  of  high  mountains  are  always 
covered  with  snow. 

The  limits  of  perpetual  snow  naturally  lie  higher  in  proportion 
as  we  approach  the  torrid  zone. 

The  height  of  the  snow-line  is  as  follows : 

The  coast  of  Norway      .  720  metres  2340  feet 

Iceland          ...  936  "  3042  " 

The  Alps       .         .         .  2708  «  8801  " 

Mount  Etna  .         .         .  2905  «  9441  « 

The  Himalayas      .         .  4500  "  14625  « 

Mexico          .         .         .  4500  « 

Quito    ....  4800  «  15600 

[These  estimates  are  lower  than  those  given  by  other  authors. 
It  is  generally  stated  that  the  snow  limit  on  the  Himalayas  is 
17,000  feet,  and  in  Mexico  14,700  to  15,030  feet.] 


49 


578    ON    THE    PRESSURE    OF    THE    ATMOSPHERE    AND    WINDS. 


CHAPTER    II. 

ON  THE  PRESSURE  OF  THE  ATMOSPHERE  AND  WINDS. 

WE  have  already  seen  that  the  pressure  of  the  air  is  measured 
by  the  barometer.  We,  however,  observe  constant  variations  in 
this  instrument,  indicative  of  an  alternate  decrease  and  increase 
in  the  pressure  of  the  atmosphere. 

These  variations  of  the  thermometer  are  either  periodical  or 
accidental. 

Periodical  variations  are  very  marked  in  their  character  in  the 
tropics;  for  instance,  the  thermometer  falls  from  10  A.M.  to 4  P.M., 
then  rises  until  11  P.M.  ;  falls  again  till  4  A.M.,  and  again  rises 
until  10  A.  M.  The  barometer  thus  indicates  two  daily  maxima, 
at  10  A.  M.  and  at  11  P.  M.,  and  two  minima,  at  4  A.  M.  and  at 
4  P.  M. 

The  amount  of  these  diurnal  variations  is  about  2mm  (0,0787 
inch). 

An  annual  period  of  the  fluctuations  of  the  barometer  is  also 
very  strongly  marked  within  the  tropics.  Thus,  north  of  the 
equator  the  barometer  falls  from  January  till  July,  and  then  rises 
again  from  July  to  January.  In  July  the  barometer  stands,  on  an 
average,  from  2  to  4  millimetres  (0,0787  to  0,1574  in.)  lower 
than  in  January. 

In  higher  latitudes,  the  accidental  fluctuations  of  the  barometer 
are  so  considerable  as  to  make  one  lose  sight  of  the  trifling 
periodic  variations  presented  in  these  regions.  In  order  to  decide 
whether  there  are  not  also  a  periodical  rise  and  fall  in  the  acci- 
dental oscillations  of  the  barometer,  it  is  necessary  to  compare 
the  mean  numbers  of  a  large  series  of  barometric  observations 
made 'at  regularly  settled  hours  of  the  day.  If  we  observe  the 
barometer  for  the  term  of  a  month  at  several  fixed  hours  of  the 
day,  and  take  the  mean  of  all  the  observations,  it  will  suffice  to 
prove  the  existence  of  a  diurnal  period  of  the  fluctuations  of  the 
barometer  even  for  our  own  region. 

Observations  of  this  kind  have  proved  that  these  periodical 


CAUSES    OF    OSCILLATIONS    IN    THE    BAROMETER.         579 

oscillations  occur  even  in  our  latitude,  the  barometer  standing  at 
9  A.M.,  on  an  average,  0,7  millimetres  (0,027  in.)  higher  than  at 
2  P.M.;  the  mean  height  of  the  barometer  is  also  somewhat  less  in 
summer  than  in  winter. 

Causes  of  the  Oscillations  in  the  Barometer. — The  cause  of  all 
these  oscillations  is  to  be  sought  for  in  the  unequal  and  constantly 
varying  distribution  of  heat  over  the  earth's  surface.  As  the 
distribution  of  heat  constantly  varies,  the  equilibrium  is  likewise 
disturbed  at  every  moment,  and  currents  of  air  arise  which  strive 
to  restore  the  balance ;  the  air  is  thus  in  constant  motion,  some- 
times more  heated,  and  then  lighter,  and  at  other  times  more  cooled, 
and  consequently  denser.  As  it  contains  sometimes  more,  some- 
times less  vapor,  the  pressure  of  the  columns  of  air  will  also  be 
exposed  to  continual  changes,  indicated  by  the  barometer. 

That  actual  changes  of  temperature  are  really  the  causes  of  the 
oscillations  of  the  barometer,  is  proved  by  their  being  most  incon- 
siderable in  the  tropics,  where  the  temperature  varies  so  little ; 
in  higher  latitudes,  on  the  contrary,  where  the  variations  of  tem- 
perature are  always  more  considerable,  the  amplitude  of  the  acci- 
dental oscillations  of  the  barometer  is  likewise  very  great:  even 
in  summer,  when  the  temperature  is  generally  less  changeable, 
the  oscillations  of  the  barometer  are  less  than  in  winter. 

Although  we  may  generally  show  that  the  unequal  and  con- 
stantly varying  temperature  of  the  air  must  be  followed  by  con- 
stant ch-anges  in  the  amount  of  the  atmospheric  pressure,  we  are, 
however,  still  far  from  being  able,  satisfactorily,  to  explain  these 
phenomena. 

If  the  air  is  much  heated  at  any  spot,  it  expands;  the  column 
of  air  rises  above  the  mass  of  air,  and  rests  upon  the  colder  parts 
surrounding  it;  the  ascended  air,  consequently,  flows  off  laterally 
from  above,  the  pressure  of  the  air  must  decrease  at  the  warmer 
places,  and  the  barometer  sinks ;  in  the  colder  parts,  however,  the 
barometer  ascends,  because  the  laterally  diffused  air,  in  the  upper 
regions  of  the  heated  places,  is  distributed  over  the  atmosphere  of 
the  cooler  parts. 

We  hence  see  why,  in  our  districts,  the  barometer  stands,  on  an 
average,  lowest  with  a  south-west  and  highest  with  a  north-east 
wind :  the  former  winds  bring  us  warm,  and  the  latter  cold,  air. 
Whenever  there  is  a  warm  current  of  air,  the  atmosphere  must 
have  a  greater  height  than  where  the  cold  wind  prevails,  if  the 


580         CAUSES    OF   OSCILLATIONS   IN   THE   BAROMETER. 

pressure  of  the  whole  column  of  air  is  to  be  equal  at  both  places; 
and  if  such  were  actually  the  case,  the  air  of  the  warm  current 
would  flow  off  from  above,  consequently  the  barometer  would  fall 
when  exposed  to  the  warm,  and  rise  when  exposed  to  the  cold. 

In  Europe,  south-west  winds,  generally,  are  the  ones  which 
bring  rain,  because,  coming  from  warmer  seas,  they  are  satu- 
rated with  vapor,  which,  gradually  condensing,  falls  as  rain  when 
the  wind  reaches  colder  districts.  In  this  condensation  of  vapor, 
we  have  another  reason  why  the  barometer  falls  with  the  south- 
west winds.  As  long,  for  instance,  as  the  vapor  of  water,  as  a 
gas,  forms  a  constituent  of  the  atmosphere,  it  contributes  to  the 
atmospheric  pressure,  and  thus  a  portion  of  the  column  of  mer- 
cury in  the  barometer  is  sustained  by  the  vapor,  and  the  baro- 
meter falls  when  the  vapor  is  separated  by  condensation  from  the 
atmosphere. 

As  the  south-west  winds,  which  occasion  a  sinking  of  the  baro- 
meter in  our  latitudes,  bring  a  damp  air  and  rainy  weather,  whilst 
the  north-east  winds,  which- dry  the  air  and  clear  the  sky,  cause 
the  barometer  to  rise,  we  may  say,  that,  in  general,  a  high  state  of 
the  barometer  indicates  fine  weather,  whilst  its  depressed  condi- 
tion forebodes  the  contrary.  This  is,  however,  only,  as  we  have 
before  remarked,  an  average  rule,  for  the  sky  is  often  cloudy  with 
a  north-east  wind,  and  clear  with  one  coming  from  the  south- 
west; the  statement  is  in  so  far  true  as  that  the  barometer  stands 
high  or  low  according  to  which  of  these  two  winds  prevails,  the 
remark  in  the  latter  case  being  nearly  true  on  an  average.  We 
are  unable  to  account  for  such  anomalies,  from  our  insufficient 
knowledge  of  the  manifold  elements  which  affect  the  condition  of 
equilibrium  of  the  atmosphere. 

That  a  high  state  of  the  barometer  generally  indicates  clear 
weather,  and  a  fall  of  the  mercury  in  the  barometer  tube  the 
contrary,  is  only  true  for  those  places  where  the  wrarm  winds  are 
those  which  bring  the  rain.  At  the  mouth  of  the  river  La  Plata, 
for  instance,  the  cold  south-east  winds  coming  from  the  sea,  and 
which  cause  the  barometer  to  rise,  are  winds  which  bring  rain, 
while  the  warm  north-west  winds,  that  make  the  barometer  fall, 
are  dry  land-winds,  and  bring  clear  weather.  To  the  cause  that 
rain  is  here  conveyed,  by  cold  winds,  is  to  be  ascribed  the  small 
quantity  of  rain  in  these  regions ;  whilst,  at  the  same  latitude,  on 


ORIGIN   OF    THE    WINDS. 


581 


Fig.  520. 


the  western  coast  of  South  America,  much  rain  falls,  although 
here,  too,  the  warm  north-west  wind  comes  from  the  sea. 

Origin  of  the  Winds.— If  in  winter  we  partially  open  the  door 
of  a  heated  apartment  communi- 
cating with  a  cold  space,  and  hold 
a  burning  taper  to  the  upper  part 
of  the  crevice  (as  seen  in  Fig.  520), 
the  outward  direction  of  the  flame 
will  indicate  the  presence  of  a  cur- 
rent of  air  passing  from  the  heated 
apartment  into  the  cooler  atmo- 
sphere. As  we  move  the  taper 
downward,  the  flame  will  con- 
stantly become  more  and  more  up- 
right ;  until  at  about  the  middle  of 
the  height  it  will  remain  perfectly 
still,  being  no  longer  affected  by 
currents  of  air.  On  moving  it 
downward,  however,  the  flame  will  be  driven  inward.  We  thus 
see  that  the  heated  air  flows  out  at  the  top  of  the  room,  whilst  the 
cold  air  enters  near  the  floor. 

As  here  the  unequal  warming  of  the  two  spaces  gives  rise  to 
currents  of  air  on  a  small  scale,  so  does  the  unequal  and  ever- 
changing  warming  of  the  earth's  surface  give  rise  to  those  currents 
of  air  which  we  call  winds.  Here,  too,  we  may  see  the  air  ascend 
in  the  more  heated  regions,  and  flow  off  towards  the  colder  parts, 
whilst,  below,  the  air  flows  from  the  colder  to  the  wanner  regions. 

We  have  a  simple  illustration  of  this  in  those  land  and  sea- 
winds,  which  we  so  frequently  observe  on  the  sea-shore,  especially 
of  islands.  A  few  hours  after  sunrise  a  land-wind  sets  in  from 
the  sea,  owing  to  the  land  being  more  strongly  heated  than  the 
sea  by  the  sun's  rays ;  the  air  rises  over  the  land,  and  flows  to- 
wards the  sea,  while,  from  below,  the  air  is  borne  from  the  water 
towards  the  shore.  This  sea-wind  is  at  first  but  light,  and  only 
perceptible  on  the  coast ;  by  degrees,  however,  it  increases,  and 
then  it  may  be  felt  out  at  sea  at  a  considerable  distance  from  land ; 
between  2  and  3  P.  M.  it  is  strongest,  afterwards  dying  away, 
until,  at  sunset,  a  calm  sets  in.  The  land  and  sea  are  now 
cooled  by  the  radiation  of  heat  towards  the  sky,  the  former, 
however,  more  rapidly  than  the  latter,  and  the  air  then  flows 

49* 


582  TRADE-WINDS    AND   MONSOONS. 

towards  the  sea  from  the  lower  regions  of  the  land,  whilst  an 
oppositely  directed  current  is  perceptible  in  the  upper  regions  of 
the  air. 

A  rapid  condensation  of  atmospheric  vapor  is  also  to  be  reckoned 
amongst  the  causes  which  give  rise  to  violent  storms.  When  we 
consider  what  an  enormous  mass  of  water  falls  to  the  ground 
during  a  sharp  shower  of  rain  in  the  course  of  a  few  minutes,  and 
what  an  enormous  volume  this  water  must  have  comprised  when 
suspended  in  the  air  in  the  form  of  vapor,  it  appears  evident  that 
a  considerable  rarefaction  of  the  air  must  be  occasioned  by  this 
sudden  condensation  of  vapor,  and  that  it  must  rush  with  violence 
into  the  rarefied  space,  the  more  so,  as  owing  to  the  condensation 
of  the  vapor,  the  temperature  of  the  air  is  raised  by  the  liberated 
heat,  and  a  strong  rising  current  thus  engendered. 

We  often  observe  the  clouds  pass  in  a  direction  different  from 
the  one  indicated  by  the  weather-cock,  and  that  the  higher  clouds 
move  in  an  opposite  direction  to  those  below  them,  whence  it  is 
evident  that,  at  different  elevations,  currents  of  air  move  in  con- 
trary directions. 

Trade-winds  and  Monsoons. — When  Columbus,  on  his  voyage 
of  discovery  towards  America,  saw  that  his  ship  was  driven  on  by 
a  continual  east  wind,  his  companions  became  filled  with  terror, 
as  they  feared  they  should  never  be  able  to  return  to  Europe. 
This  wind  of  the  tropics,  which  constantly  blows  from  the  east 
to  the  west,  and  so  greatly  excited  the  wonder  of  the  first  navi- 
gators of  the  15th  century,  is  the  trade-wind.  Seamen  avail  them- 
selves of  this  wind  to  sail  from  Europe  to  America,  by  steering 
southward  from  Madeira  to  the  vicinity  of  the  tropic,  where  they 
are  then  carried  westward  by  the  trade-wind.  This  course  is  so 
certain,  and  attended  with  so  little  labor,  that  the  Spanish  sailors 
gave  the  name  of  Ladies'  Gulf  (el  Golfo  de  las  Damas)  to  this 
portion  of  the  Atlantic  Ocean.  This  wind  also  blows  in  the  South 
Sea,  and  the  Spanish  navigators  let  their  ships  be  propelled  by  it 
in  a  straight  line  from  Acapulco  to  Manilla. 

In  the  Atlantic  Ocean  the  trade- winds  extend  from  28°  to  30° 
lat.;  but  in  the  great  ocean  (the  Pacific)  only  to  25°  N.  lat.  In 
the  northern  half  of  the  torrid  zone,  the  trade-wind  blows  in  a 
north-east  direction,  and  becomes  more  decidedly  east  as  it  ap- 
proaches the  equator.  The  limits  of  the  trade-wind  are  less  well 
defined  in  the  southern  hemisphere,  where  it  has  a  south-east 


TRADE-WINDS    AND   MONSOONS.  583 

direction,  and  inclines  more  towards  due  east  the  more  it  ap- 
proaches the  equator. 

These  winds  blow  round  the  whole  globe ;  but,  as  a  general 
rule,  they  do  not  become  perceptible  within  fifty  German  miles 
from  the  land. 

Where  the  north-east  trade-wind  meets  the  south-east  trade-wind 
of  the  southern  hemisphere,  the  two  merge  into  a  purely  eastern 
wind ;  which,  however,  is  not  perceptible,  because  the  horizontal 
motion  of  the  air  (which  has  been  heated  by  the  intensity  of  the 
sun's  rays,  and  thus  made  to  ascend),  is  neutralized  by  this  ver- 
tical motion.  There  would  be  almost  a  perfect  calm  in  these 
regions  if  the  violent  storms  accompanying  the  torrents  of  rain, 
which  occur  almost  daily  with  thunder  and  lightning,  were  not 
to  disturb  the  calm  of  the  atmosphere,  and  prevent  the  blowing  of 
soft  regular  winds. 

This  zone,  which  separates  the  trade-winds  of  both  hemispheres, 
is  the  region  of  calms. 

The  little  map,  seen  in  Fig.  521,  serves  to  indicate  the  regions 

Fig.  521. 


in  which  the  trade-winds  prevail.  The  middle  of  the  region  of 
calms,  extending  about  6°  in  width,  does  not  coincide  with  the 
equator,  as  we  might  be  led  to  expect,  but  lies  to  the  north  of  it. 
During  our  summer  months,  the  zone  of  these  calms  is  broader, 
and  its  northern  boundary  is  further  removed  from  the  equator, 
whilst  its  southern  line  is  but  little  changed. 

The  cause  why  the  region  of  calms  lies  in  the  northern  hemi- 
sphere, may  be  sought  for  in  the  configuration  of  the  continent. 

The  trade  winds  may  be  easily  explained.  The  air  that  has 
been  strongly  heated  in  "the  equatorial  regions  ascends,  and  rising 


584  TRADE-WINDS    AND    MONSOONS. 

over  the  colder  masses  of  air  on  either  side,  flows  upwards 
towards  the  poles,  whilst  below,  it  flows  from  the  poles  towards 
the  equator.  If  the  earth  did  not  rotate  on  its  axis,  the  trade- 
wind  in  the  northern  hemisphere  would  blow  directly  from  north 
to  south,  while  in  the  southern  hemisphere  its  direction  would 
be  opposite.  The  earth,  however,  rotates  from  west  to  east,  and 
the  atmosphere  surrounding  it  partakes  of  this  rotatory  motion. 

The  nearer  a  place  upon  the  earth's  surface  is  to  the  poles,  the 
slower  will  it  move  during  its  twenty-four  hours'  revolution,  be- 
cause the  space  it  describes  diminishes  as  it  recedes  from  the 
equator.  The  rotatory  velocity  of  the  mass  of  air  over  the  earth, 
is,  consequently,  less  near  the  poles  than  it  is  at  the  equator;  if, 
then,  a  mass  of  air  comes  from  higher  latitudes  to  the  equator,  it 
will  pass  over  districts  with  a  less  velocity  of  rotation  than  that 
with  which  these  move  from  west  to  east ;  in  relation  to  the  places 
rotating  below  it,  it  will,  therefore,  have  a  motion  from  east  to 
west.  This  motion  combines  with  the  motion  towards  the  equator 
to  produce  a  north-east  in  the  northern,  and  a  south-east  wind  in 
the  southern,  hemisphere. 

The  air  which  rises  in  the  equatorial  regions  flows  off  on  either 
side  towards  the  direction  of  the  poles.  The  course  of  the  upper 
trade-wind  is  naturally  directly  opposite  to  that  of  the  lower  one, 
being  south-west  in  the  northern,  and  north-west  in  the  southern, 
hemisphere. 

We  may  prove  by  facts,  that  there  is  actually  a  trade-wind 
in  the  upper  regions  of  the  air;  thus,  for  instance,  on  the  25th  of 
February,  1835,  at  an  eruption  of  the  volcano  of  Cosiguina,  in  the 
State  of  Guatimala,  the  ashes  were  ejected  to  the  elevation  of  the 
upper  trade-wind,  and  were  carried  by  it  in  a  south-west  direc- 
tion, and  precipitated  on  the  island  of  Jamaica,  although  the  north 
trade-wind  was  blowing  in  the  regions  below. 

At  a  greater  distance  from  the  equator,  however,  the  upper 
trade-wind  inclines  more  and  more  towards  the  earth's  surface. 
At  the  summit  of  the  Peak  of  Teneriflfe,  west  winds  almost  always 
prevail,  whilst  the  lower  trade-wind  blows  at  the  level  of  the  sea. 

In  the  Indian  Ocean,  the  regularity  of  the  trade-winds  is  dis- 
turbed by  the  configuration  of  the  land  surrounding  this  sea — for 
instance,  by  the  Asiatic  continent.  In  the  southern  part  of  the 
Indian  Ocean,  between  New  Holland  and  Madagascar,  the  south- 
east trade-wind  prevails  throughout  the  year,  while  a  constant 


WINDS    IN    HIGHER    LATITUDES.  585 

south-west  wind  blows  in  the  northern  part  of  this  ocean  during 
six  months  of  the  year,  and  a  constant  north-east  wind  during  the 
remaining  period  of  the  year.  These  regularly  alternating  winds 
are  called  monsoons. 

The  south-west  wind  blows  from  April  till  October,  while  the 
north-east  wind  prevails  during  the  other  months. 

As  during  the  winter  the  Asiatic  continent  is  cooled,  while  a 
greater  heat  is  engendered  in  the  southern  regions,  a  north-east 
trade-wind  must  naturally  pass  from  the  colder  parts  of  Asia  to 
hotter  regions.  At  this  time,  too,  the  north-east  trade-wind  is 
separated  from  the  south-west  trade-wind,  in  the  Indian  Ocean, 
by  the  region  of  calms. 

During  the  summer  months,  the  passage  of  the  south-east  trade- 
wind  between  New  Holland  and  Madagascar,  is  not  disturbed, 
whilst,  in  the  northern  parts  of  the  Indian  Ocean,  the  wind  that 
had  blown  during  the  winter  from  the  north-east,  is  now  changed 
into  a  south-west  wind,  owing  to  the  Asiatic  continent  becoming 
so  strongly  heated,  and  a  current  of  air  being  thus  conveyed 
towards  the  north,  which,  by  the  rotation  of  the  earth,  is  converted 
into  a  south- wrest  wind. 

Winds  in  Higher  Latitudes. — The  upper  trade-wind,  which 
brings  the  air  from  the  equatorial  regions,  falls  more  and  more, 
as  has  been  already  mentioned,  and,  finally,  reaches  the  earth  as 
a  south-west  wind ;  when  beyond  the  region  of  the  trade- winds, 
the  two  currents  of  air  that  pass  from  the  poles  to  the  equator,  and 
back  from  the  equator  to  the  poles,  no  longer  blow  over,  but  even 
with  each  other  endeavoring  to  replace  one  another;  thus,  on  the 
south-west  or  the  north-east  wind  predominating  from  time  to 
time,  we  see,  on  the  transition  of  the  wind  from  one  direction  to 
another,  the  currents  of  air  moving  in  all  points  of  the  weather- 
cock. 

Although  the  south-west  and  north-east  winds  predominate  also 
in  higher  latitudes,  we  find  no  regularly  periodic  alternation  in 
their  occurrence,  as  is  the  case  with  the  monsoons  in  the  Indian 
Ocean. 

The  following  table  indicates  the  frequency  of  the  winds  in 
different  countries;  giving  the  number  of  average  times  that  each 
wind  blows  during  every  one  thousand  days. 


586 


LAWS    OF    THE    CHANGE    OF    WIND. 


Countries. 

N. 

N.E. 

E. 

S.E. 

S. 

S.W. 

W. 

N.W. 

England 

82 

Ill 

99 

81 

Ill 

225 

171 

120 

France  . 

126 

140 

84 

76 

117 

192 

155 

110 

Germany 

84 

98 

119 

87 

97 

185 

198 

131 

Denmark 

65 

98 

100 

129 

92 

198 

161 

156 

Sweden  . 

102 

104 

80 

110 

128 

210 

159 

106 

Prussia  . 

99 

191 

81 

130 

98 

143 

166 

192 

N.  America 

96 

116 

49 

108 

123 

197 

101 

210 

Laws  of  the  Change  of  Wind. — Although  the  changes  in  the 
direction  of  the  wind  appear,  on  a  superficial  view,  to  be  wholly 
devoid  of  rule  in  our  regions,  attentive  observers  have  long  since 
made  the  remark  that  winds  generally  succeed  each  other  in  the 
following  order : 

S.  SW.  W.  JYW.  JV.  WE.  E.  SE.  S. 

This  alternation  in  the  winds  may  be  the  most  regularly 
observed  during  the  winter.  The  changes  of  the  barometer  and 
thermometer,  which  are  connected  with  these  changes  of  wind, 
have  been  well  described  by  Dove,  in  the  following  words. 

"  When  the  south-west  wind,  constantly  increasing  in  force,  at 
length  predominates,  it  raises  the  temperature  above  the  freezing 
point;  and  the  snow  is  consequently  converted  into  rain,  whilst 
the  barometer  falls  to  the  lowest  mark.  The  wind  then  veers 
round  to  the  west,  and  the  dense  flakes  of  snow  indicate  the 
accession  of  a  colder  wind  no  less  than  the  rapid  rise  of  the 
barometer,  the  motion  of  the  weather-cock,  and  the  thermometer. 
A  north  wind  clears  the  heavens,  and  a  north-east  wind  effects 
a  maximum  of  cold,  and  of  the  barometer.  This,  however,  is 
gradually  lowered,  and  the  occurrence  of  fine  cirri  indicates  by 
the  direction  from  which  they  come,  the  advent  of  a  more  southern 
wind,  which  is  soon  felt  by  the  barometer,  although  the  weather- 
cock may  not  have  experienced  any  change,  and  may  still  be 
pointing  due  east.  The  southern  wind,  however,  continues  to 
drive  the  eastern  current  downward,  and  on  a  decided  falling  of 
the  mercury,  the  weather-cock  points  south-east,  when  the  heavens 
again  become  gradually  overcast,  and  with  the  increase  of  heat, 
the  snow  that  had  fallen  with  a  south-east  and  south  wind,  is 
again  converted  into  rain  by  the  south-west  wind.  The  same 
then  begins  again,  the  change  from  the  east  to  the  west  course 
being  generally  characterized  by  the  occurrence  of  a  short  interval 
of  fine  weather." 

The  shifting  of  wind  does  not  always  admit  of  being  as  regu- 


LAWS  OF  THE  CHANGE  OF  WIND.  587 

larly  traced  as  is  indicated  above,  there  being  often  a  recurrence 
of  the  wind  to  its  old  quarter ;  this,  however,  is  far  more  fre- 
quently observed  in  the  west  than  the  eastern  points  of  the  com- 
pass. A  perfect  change  of  the  wind  in  an  opposite  direction,  as 
from  south  to  east,  north  or  west,  is  very  rarely  observed  in 
Europe. 

The  explanation  of  this  law  is  obtained  by  the  generalization 
of  the  explanation  concerning  the  trade-winds. 

If  the  air  from  any  cause  be  driven  from  the  poles  towards  the 
equator,  it  will  pass  from  places  having  but  an  inconsiderable 
rotatory  velocity,  to  such  as  possess  a  greater  degree  of  speed ;  and 
its  motion  will  thus  acquire  an  eastern  direction,  as  we  have 
seen  in  the  case  of  the  trade-wind.  On  the  northern  hemisphere 
the  winds  which  arise  in  the  north  pass  therefore,  in  their  gradual 
progress,  through  the  north-east  to  the  east.  If  an  east  wind  thus 
arise,  it  will,  if  the  same  causes  continue  in  operation  which  have 
driven  the  air  towards  the  equator,  act  retardingly  upon  the  polar 
current ;  the  air  will  acquire  the  same  speed  of  rotation  as  the 
place  over  which  it  passes ;  and  if  the  tendency  to  return  to  the 
equator  still  continue,  the  wind  will  shift  back  to  the  north,  when 
the  same  series  of  phenomena  will  be  repeated. 

If,  however,  after  the  polar  current  has  predominated  for  a  time, 
and  the  direction  of  the  wind  has  become  eastern,  currents  set  in 
from  the  equator,  the  east  wind  will  pass  from  south-east  to  the 
south.  If  the  air  move  from  south  to  north,  it  will  reach  places 
having  an  inconsiderable  velocity  of  rotation  with  the  greatest 
velocity  of  rotation  of  the  polar  regions  nearest  the  equator ; 
hastening,  as  it  were,  in  advance  of  the  earth's  surface  which 
rotates  from  west  to  east,  until  the  southern  direction  of  the  wind 
is  gradually  changed  to  the  south-west,  and  finally  made  quite 
western.  By  the  constant  tendency  of  the  air  to  pass  towards  the 
poles,  the  wind  is  made  to  veer  back  again  to  the  south,  exactly 
in  the  same  manner  as  the  east  wind  veers  to  the  north ;  if,  how- 
ever, the  equatorial  current  be  displaced  by  a  current  from  the 
poles,  the  west  wind  will  veer  from  north-west  round  to  the  north. 
In  the  southern  hemisphere,  the  wind  must  necessarily  veer 
about  in  an  opposite  direction. 

Where  the  trade-winds  blow  in  the  tropics,  there  is  no  com- 
plete rotation  on  the  earth's  surface ;  the  direction  of  the  trade- 


588  STORMS. 

wind  is,  therefore,  only  inclined  more  towards  the  east  in  its 
motion. 

In  the  region  of  the  monsoon,  there  is  only  one  complete  rota- 
tion in  the  course  of  the  whole  year.  We  therefore  see  that  the 
relations  of  the  winds  in  the  tropics  correspond  to  the  simplest 
case  of  the  law  of  rotation. 

Storms. — Storms  are  the  result  of  a  considerable  disturbance  in 
the  equilibrium  of  the  atmosphere,  depending  very  probably  upon 
a  rapid  condensation  of  vapor,  as  has  already  been  surmised. 

More  recent  investigations  have  shown  that  storms  may,  for  the 
most  part,  be  regarded  as  great  whirlwinds  in  motion. 

Storms  rage  with  much  more  violence  in  the  tropics  than  in 
higher  latitudes  ;  the  devastations  occasioned  by  these  hurricanes, 
known  in  America  by  the  name  of  Tornadoes,  are  truly  frightful. 
Thus,  for  instance,  in  the  hurricane  that  devastated  Guadaloupe 
on  the  25th  of  July,  solidly-built  houses  were  torn  up ;  cannons 
were  hurled  from  the  top  of  the  parapets  of  the  batteries  on  which 
they  were  planted  ;  a  plank  of  about  3  feet  in  length,  8  inches  in 
breadth,  and  10  lines  in  thickness,  was  propelled  with  such  force 
through  the  air  that  it  perforated  the  stem  of  a  palm  tree,  about 
17  inches  in  diameter,  through  and  through. 

We  often  see  how,  in  calm  weather,  sand  and  dust  are  carried 
by  the  wind  with  a  whirling  motion  through  the  air.  On  the  ap- 
proach of  a  storm,  we  may  also  notice  larger  whirlwinds  of  this 

Fig.  522. 


ATMOSPHERIC    MOISTURE.  589 

kind  carrying  sand,  dust,  leaves,  and  straw,  &c.,  with  them  in 
their  course.  Hurricanes  are  nothing  more  than  these  whirlwinds 
on  a  large  scale,  and  are  generally  caused  by  the  struggle  of  two 
winds  moving  in  opposite  directions  in  the  upper  regions  of  the 
air.  They  usually  form  a  double  cone,  the  upper  part  of  which, 
whose  vertex  inclined  downwards,  consists  of  a  mass  of  clouds; 
while  the  lower  cone,  the  point  of  which  is  directed  upward,  when 
formed  over  the  sea,  lakes  and  rivers,  is  composed  of  water  or  of 
sand,  and  other  bodies  found  on  land.  These  hurricanes  are 
capable  of  uprooting  trees,  unroofing  houses,  and  hurling  beams 
to  a  distance  of  many  hundred  paces,  &c.  Water  hurricanes  are 
known  as  water  spouts ;  they  often  raise  water  to  the  height  of 
many  hundred  feet. 


CHAPTER   III. 

OF    ATMOSPHERIC     MOISTURE. 

Distribution  of  Vapor  in  the  Mr.— If,  on  a  hot  summer's  day, 
we  place  a  bowl  filled  with  cold  water  in  the  open  air,  we  observe 
that  the  quantity  of  the  water  rapidly  diminishes, — that  is,  it  eva- 
porates, which  means  that  it  is  converted  into  vapor,  and  then 
diffused  through  the  air.  The  vapor  of  water  is,  like  every  other 
colorless  transparent  gas,  invisible  to  our  eyes,  the  water  appear- 
ing to  have  entirely  disappeared  by  evaporation. 

The  water  diffused  through  the  air  only  becomes  visible  when, 
on  returning  to  its  fluid  condition,  it  forms  a  mist,  cloud,  dew,  or 
hoar-frost.  In  order,  therefore,  to  convince  ourselves  of  the  ex- 
istence of  vapor  of  water  in  the  air,  we  must  condense  it  by  some 
means  or  another. 

We  may  immediately  obtain  the  quantity  of  vapor  contained  i 
a  definite  volume  of  air,  on  sucking  the  air  through  a  tube  filled 
with  hygrometric  substances.  We  make  use  of  an  aspirator  for 
the  purpose  of  effecting  a  regular  passage  of  the  air  through  the 
absorption  tube.  The  aspirator  is  a  vessel  filled  with  water,  and 
50 


590 


DISTRIBUTION    OF    VAPOR    IN    THE    AIR. 


closed,  excepting  at  two  apertures  ;  from  the  one  of  which  water 
constantly  pours  out  through  a  tube,  while  the  other  is  connected 
with  the  absorption  tube  in  such  a  manner,  that  an  amount  of 
dry  air  equal  to  the  discharged  water  may  enter  the  vessel.  The 
amount  of  vapor  contained  in  a  quantity  of  air  sucked  through 
the  absorption  tube,  may  be  ascertained  by  weighing  the  tube 
before  and  after  the  experiment. 

This  method  of  determining  the  quantity  of  water  contained 
in  the  air  entering  the  aspirator,  to  which  various  forms,  more  or 
less  applicable,  have  been  given,  is  somewhat  uncertain,  and  does 
not  yield  the  amount  of  water  contained  in  the  air  at  a  definite 
moment,  but  merely  the  mean  average  of  its  quantity  during  the 
whole  period  of  the  experiment;  on  this  account,  smaller  and  more 
easily  transportable  apparatuses  have  been  constructed,  which  are 
known  by  the  name  of  hygrometers. 

It  is  well  known  that  many  organic  bodies  have  the  property  of 
absorbing  vapor,  and  thus  increasing  proportion  ably 
in  extent.  Amongst  others,  we  may  mention  hair, 
whalebone,  &c.,  as  hygrometric  bodies,  and  these 
have,  therefore,  been  employed  in  the  construction 
of  hygrometers.  The  best  instrument  of  the  kind 
is  the  Hair-hygrometer  invented  by  Saussure,  and 
which  is  represented  in  Fig.  523. 

The  hair  is  fastened  at  its  upper  end  to  a  little 
tongue  a ;  the  other  extremity  passes  over  along  one 
of  the  two  grooves  of  a  pulley ;  while  in  the  other 
groove  a  silk  thread  goes  round  the  pulley,  sup- 
porting a  little  weight  f,  by  means  of  which  the 
hair  is  kept  at  a  constant  tension.  To  the  axis  of 
the  pulley,  an  index  d  is  attached,  which  passes 
over  the  graduated  arc  s  h,  as  the  pulley  is  turned  by  the  elonga- 
tion or  shortening  of  the  hair. 

When  the  instrument  is  in  a  damp  atmosphere,  the  hair  absorbs 
a  considerable  amount  of  vapor,  and  is  thus  made  longer,  while 
in  a  dry  air  it  becomes  shorter,  so  that  the  index  is  of  course 
turned  alternately  to  the  one  or  to  the  other  side. 

The  instrument  is  graduated  in  the  following  manner.  In  the 
first  place,  it  is  placed  under  a  receiver,  the  air  within  having 
been  dried  by  chloride  of  calcium  or  by  sulphuric  acid.  The 


DANIEL'S    HYGROMETER.  591 

point  of  the  scale  at  which  the  index  stops,  under  these  circum- 
stances, is  the  point  of  greatest  dryness,  and  is  marked  with  0. 

The  instrument  is  then  placed  under  a  receiver,  whose  walls 
are  moistened  with  distilled  water,  which  is  likewise  poured  upon 
the  ground,  on  which  the  receiver  is  placed.  The  space  below 
it  soon  becomes  saturated  with  vapor,  and  the  index  then  passes 
to  the  other  end  of  the  scale.  The  point  at  which  it  now  stands, 
is  the  point  of  greatest  moisture,  and  is  marked  100. 

The  space  intervening  between  these  two  points  must  then 
be  divided  into  100  equal  parts,  which  are  termed  degrees  of 
moisture. 

The  relation  of  these  degrees  to  the  quantity  of  water  in  the  air, 
must,  in  the  case  of  every  instrument  of  the  kind,  be  ascertained 
by  means  of  experiments,  into  which  we  cannot  enter  more  fully 
at  present. 

DanieVs  Hygrometer  is  represented  in  Fig.  524;  it  consists 
of  a  curved  tube  terminating  in  two  bulbs ;  Fi  524 

the  one  a  is  either  gilt,  or  covered  with  a 
thin  metallic  coating  of  platinum,  while 
the  other  is  wrapped  in  a  piece  of  fine 
linen.  The  bulb  a  is  half  filled  with 
ether,  and  contains  a  little  thermometer, 
the  graduated  part  of  which  penetrates 
into  the  tube  t.  The  apparatus  is  per- 
fectly air-tight.  If  ether  be  dropped  upon 
the  ball  b,  it  will  cool  it  by  its  evaporation ; 
in  the  interior  the  vapor  of  the  ether  will 
be  condensed,  and  an  evaporation  in  the 

bulb  a  thus  occasioned,  since,  to  a  certain  degree,  the  ether  dis- 
tils over  from  the  warmer  ball  a,  to  the  cooler  one  b.  By  the 
formation  of  vapor  in  the  ball  a,  heat  will  be  likewise  absorbed, 
and  the  bulb  become  covered  with  a  delicate  dew.  The  origin 
of  this  dew  admits  of  an  easy  explanation.  We  have  seen  above, 
that  in  a  vacuum,  the  force  of  tension  of  steam  cannot  exceed 
certain  limits,  and  that  the  maximum  of  the  tension  increases 
with  the  temperature.  For  a  temperature  of  68°  (154°  F.),  for 
instance,  the  maximum  of  the  force  of  tension  of  steam  is  17,3 
millimetres  (.633  in.),  and  the  corresponding  density  of  the  steam 
0,00001718 ;  in  a  vacuum  of  1  cubic  metre  (27.0.3  cubic  ft.), 


592  DANIEL'S    HYGROMETER. 

therefore,  at  a  temperature  of  at  most  78°  (172°  F,)  17,18  grms. 
(264.93  grs.)  of  water  may  be  contained  in  the  form  of  vapor. 

We  have,  however,  further  seen,  that  exactly  as  much  steam 
may  be  contained  in  a  space  filled  with  air  as  in  an  equally  large 
vacuum,  and  that,  in  this  case,  the  force  of  tension  of  the  air,  and 
the  force  of  tension  of  the  steam  diffused  through  it,  correspond. 
At  a  temperature  of  78°  (172°  F,),  17,18  grms.  (264.93  grs.)  of 
water  may,  therefore,  be  contained  as  vapor  in  1  cubic  metre  of 
air  (27.0.3  cubic  ft.). 

We  say  the  air  is  saturated  with  vapor,  when  the  steam  diffused 
through  it  has  reached  the  maximum  of  the  force  of  tension  and 
density  corresponding  with  its  temperature. 

If  we  bring  a  colder  body  into  an  atmosphere  saturated  with 
moisture,  it  will  cool  the  strata  of  air  most  contiguous ;  a  portion 
of  the  vapor  contained  will  be  condensed,  and  precipitated  upon 
the  cold  body  in  the  form  of  fine  drops.  In  this  manner  the 
moisture  which  covers  the  window  panes  of  an  inhabited  heated 
apartment  is  formed,  if  the  temperature  of  the  external  air  be  low 
enough  sufficiently  to  cool  the  panes  of  glass. 

The  air  is  not  always  saturated  with  moisture,  that  is  to  say,  it 
does  not  alwrays  contain  as  much  vapor  as  from  its  temperature 
it  might  take  up.  If,  for  instance,  we  assume  that  every  cubic 
metre  of  air  contains  only  13,63  grms.  (210.49  grs.)  of  steam  at 
a  temperature  of  78°  (172°  F.),  the  air  will  not  be  saturated, 
since  at  this  temperature,  each  cubic  metre  of  air  is  capable  of 
containing  17,18  grms.  (264.93  grs.)  of  vapor. 

The  temperature  at  which  the  condensation  of  steam  begins, 
that  is,  the  temperature  at  which  the  air  is  exactly  saturated  with 
vapor,  is  called  the  dew  point. 

DanieVs  Hygrometer  is  intended  for  the  observation  of  this  dew 
point ;  thus,  as  soon  as  the  bulb  a  is  cooled  to  the  temperature  of 
the  dew  point,  this  bulb  begins  to  be  covered  with  moisture,  and 
the  temperature  of  the  dew  point  may  be  immediately  ascertained 
from  the  thermometer  which  dips  into  the  bulb  a. 

If  we  now  make  use  of  a  table  giving  the  maximum  quantity  of 
vapor  of  water  in  a  space  of  1  cubic  metre  (27.0.3  cubic  ft.)  for 
each  degree  of  temperature,  we  may  likewise  find,  by  means  of 
such  a  table,  what  is  the  quantity  of  vapor  of  water  in  the  air  cor- 
responding to  the  dew  point  observed. 


AUGUST'S    PSYCHROMETER.  593 

August's  Psychrometer  is  represented  in  Fig.  525 ;  it  consists 
of  two  thermometers  fastened  to  one  and  the  same 
stand :  the  bulb  of  the  one  is  surrounded  by  fine 
linen,  whilst  that  of  the  other  remains  free;  on 
moistening  with  water  the  covering  of  the  one  bulb, 
the  water  will  evaporate,  and  the  more  rapidly  in 
proportion  as  the  air  is  far  removed  from  its  point 
of  saturation.  The  evaporation  of  the  water  is, 
however,  accompanied  by  an  absorption  of  heat,  in 
consequence  of  which  the  covered  thermometer  falls. 
If  the  air  be  perfectly  saturated  with  moisture,  no 
water  will  be  able  to  evaporate ;  both  temperatures, 
therefore,  will  stand  equally  high :  if,  however,  the 
air  be  not  thoroughly  saturated  with  vapor,  the  co- 
vered thermometer  will  fall  lower  in  proportion  as 
the  air  is  further  removed  from  the  point  of  satura- 
tion. We  may  judge  of  the  condition  of  moisture 
of  the  air  by  the  difference  of  temperature  of  the 
two  thermometers. 

Diurnal  and  Annual  Variation  in  the  Quantity  of  Water  contained 
in  the  Air. — As  more  vapor  may  be  diffused  through  the  air  at  a 
high  temperature,  and  as  with  an  increasing  heat  the  water  eva- 
porates more  and  more  from  the  surface  of  large  masses  of  water 
and  from  the  moist  ground,  it  may  well  be  supposed  that  the 
quantity  of  water  contained  in  the  air  will  diminish  and  increase 
in  the  course  of  the  day. 

It  has  been  ascertained  by  experiments  with  the  above-described 
instruments,  that,  in  general,  the  quantity  of  vapor  in  the  air  is 
increased  as  the  temperature  rises  with  the  ascent  of  the  sun ; 
this,  however,  only  lasts  till  9  o'clock,  when  an  ascending  cur- 
rent of  air,  occasioned  by  the  strong  heating  of  the  surface  of  the 
ground,  carries  the  vapor  on  high,  so  that  the  water  contained 
in  the  lower  strata  of  air  diminishes,  although  the  formation  of 
vapor  continues  with  the  increase  of  the  heat;  this  diminution 
continues  till  towards  4  o'clock;  now  the  quantity  of  water  of  the 
lower  strata  of  air  again  increases,  because  the  upwardly  directed 
current  of  air  ceases  to  carry  away  the  vapor  formed  ;  this  increase 
lasts,  however,  only  until  towards  9  o'clock,  because  the  decreas- 
ing temperature  of  the  air  puts  a  limit  to  the  further  formation  of 
vapor. 


594         QUANTITY   OF    WATER    CONTAINED    IN    THE    AIR. 

In  winter,  when  the  action  of  the  sun  is  less  intense,  the  state 
of  the  case  is  different ;  in  January,  we  observe  only  one  maximum 
of  the  contents  of  water  in  the  air,  at  about  2  o'clock,  and  only 
one  minimum  at  the  time  of  sunrise. 

We  say  "  the  air  is  dry"  when  water  evaporates  rapidly,  and 
when  moistened  objects  become  quickly  dry  owing  to  this  rapid 
evaporation;  and,  on  the  other  hand,  we  say  "  the  air  is  damp" 
when  moistened  objects  dry  only  slowly,  or  not  at  all,  in  the  air, 
when  the  least  decrease  of  temperature  occasions  a  precipitation  of 
moisture,  and  when  somewhat  colder  objects  become  covered  with 
moisture.  We,  therefore,  call  the  air  dry  when  it  is  far  from 
being  at  its  point  of  saturation,  and  moist  when  the  dew  point 
approaches  very  nearly  to  the  degree  of  the  temperature  of  the 
air;  in  thus  judging  of  the  dryness  or  the  dampness  of  the  air, 
we  do  not,  therefore,  express  any  opinion  of  the  absolute  quantity 
of  water  contained  in  the  air.  If  on  a  hot  summer's  day  at  a 
temperature  of  77,  every  cubic  metre  (27.0.3  cubic  ft.)  of  air  con- 
tains 13  grms.  (200.76  grs.)  of  vapor,  we  say  the  air  is  very 
dry ;  for  at  such  a  temperature  the  atmosphere  can  contain  22,5 
grms.  (339.76  grs.)  of  vapor  for  every  cubic  metre  of  air,  other- 
wise the  air  must  be  cooled  to  59,  in  order  to  be  saturated  by  the 
same  quantity  of  aqueous  vapors.  If,  on  the  contrary,  in  winter, 
at  a  temperature  of  35,6,  the  air  contains  only  6  grms.  (92.66 
grs.)  of  vapor,  it  is  very  damp,  since  the  atmosphere  is  nearly 
perfectly  saturated  with  vapor  corresponding  to  that  temperature, 
and  the  least  decrease  of  temperature  is  followed  by  a  precipita- 
tion of  moisture. 

In  this  sense  we  may  say,  that,  at  the  time  of  sunrise,  the  air 
is  the  dampest,  although  the  absolute  quantity  of  water  is  less  then 
than  at  any  other  time  of  the  day.  Towards  3  o'clock  p.  M.  in 
summer,  the  air  is  dryest. 

The  absolute  quantity  of  water  contained  in  the  air  is,  like  the 
mean  temperature  of  the  air,  at  a  minimum  in  January;  it  increases 
until  July,  when  it  reaches  its  maximum ;  then,  however,  it  again 
decreases  until  the  end  of  the  year. 

Although  the  quantity  of  water  contained  in  the  air  is  greater 
in  summer  than  in  winter,  we  say  that  the  air  is  dryer  in  summer, 
because,  on  an  average,  it  is  further  removed  from  the  point  of 
saturation  during  that  season. 


MOISTURE    OF    THE   AIR    IN    VARIOUS    DISTRICTS.         595 

Moisture  of  the  Mr  in  various  Districts. — The  formation  of 
vapor  is  especially  dependent  upon  two  conditions,  namely,  upon 
the  temperature,  and  upon  the  pressure  of  water.  With  an  un- 
limited supply  of  water,  vapor  will  be  formed  in  proportion  to  the 
height  of  the  temperature ;  but  with  equal  degrees  of  temperature, 
more  vapor  will  be  formed  in  districts  which  abound  in  water 
than  in  those  which  do  not.  Hence  it  follows,  that  the  absolute 
quantity  of  water  in  the  air,  other  circumstances  being  the  same, 
decreases  from  the  equator  to  the  poles,  and  that  the  air  is  dryer 
in  the  interior  of  large  continents,  that  is,  it  is  there  further 
removed  from  the  point  of  saturation  than  on  the  sea  or  on  the 
sea-shore.  The  clearness  of  the  sky  in  continental  countries,  is 
a  proof  that  the  dryness  of  the  air  increases  with  the  distance 
from  the  sea. 

Dew. — It  has  already  been  stated,  at  page  591 ,  that  fine  dew  is 
formed  upon  the  polished  bulb  of  DanieVs  hygrometer,  as  the  lat- 
ter is  cooled.  We  may  explain  the  formation  of  dew  on  a  large 
scale  in  a  similar  manner. 

When  in  summer,  after  sunset,  the  sky  remains  clear,  and  the 
air  calm  ;  the  different  objects  on  the  earth's  surface  become  more 
and  more  cooled  by  nocturnal  radiation  towards  the  sky ;  their 
temperature  falls  from  7°  to  23°,  or  25°  even  below  the  tempera- 
ture of  the  air;  cold  bodies  also  lower  the  temperature  of  the 
strata  of  air  immediately  surrounding  them ;  and  when  these  are 
cooled  down  to  the  dew  point,  a  portion  of  the  vapor  contained 
in  them  is  precipitated  upon  cold  bodies  in  the  form  of  fine 
drops. 

As  all  bodies  have  not  an  equal  capacity  of  radiating  heat, 
some  cool  more  perfectly  than  others,  whence  it  follows,  that 
many  bodies  may  be  densely  covered  with  dew,  whilst  others  will 
remain  almost  wholly  dry.  Grass  and  leaves,  especially,  cool 
rapidly  by  nocturnal  radiation,  partly  because  they  possess  a  very 
strong  capacity  for  radiation,  and  partly,  also,  because  they  stand 
exposed  to  the  air,  and  can  thus  receive  but  little  heat  from  the 
ground  ;  they  are  thus  more  thickly  covered  with  dew  than  stones 
and  the  bare  ground. 

When  the  sky  is  overcast  by  clouds,  the  formation  of  dew  is 
prevented,  owing  to  nocturnal  radiation  being  impeded.  Even 
when  a  somewhat  brisk  wind  blows,  no  dew  is  formed,  because 
warm  air  is  constantly  brought  into  contact  with  solid  bodies, 


596  MISTS    AND    CLOUDS. 

which  are  thus  continually  warmed,  and  allow  of  air  passing  over 
them  before  they  can  be  cooled  to  the  dew  point. 

Hoar-frost  is  nothing  but  frozen  dew.  When  the  body,  on 
which  the  condensed  vapor  is  precipitated,  is  cooled  below  32°, 
vapor  can  no  longer  be  deposited  in  a  fluid  form,  but  will  appear 
as  icicles. 

Mist  and  Clouds. — When  steam  rises  from  a  vessel  of  boiling 
water,  and  diffuses  itself  through  a  cooler  atmosphere,  it  is  imme- 
diately condensed,  and  there  arises  a  mist  in  the  air,  which  floats 
about  in  the  form  of  a  quantity  of  small  hollow  vesicles.  This 
is  also  frequently  called  vapor,  although  it  is  no  longer  such, 
at  least  in  the  physical  sense  of  the  word,  being  a  condensed 
aqueous  gas. 

When  the  condensation  of  vapor  does  not  occur  by  contact 
with  cold  solid  bodies,  but  goes  on  in  the  air,  mists  arise,  which 
are  similar  to  those  we  see  formed  over  boiling  water. 

Mists  generally  arise  when  the  water  of  lakes  and  rivers,  or  the 
damp  ground,  is  warmer  than  the  air  which  is  saturated  with 
moisture.  The  vapors  formed  in  consequence  of  the  higher  tem- 
perature of  the  water,  or  the  damp  ground,  are  immediately  re- 
condensed,  when  they  diffuse  themselves  through  the  cooler  air, 
already  saturated  with  vapor.  No  mists  are  formed  at  an  equal 
difference  of  temperature  between  the  water  and  air,  provided  the 
air  is  dry,  so  that  all  the  vapors  rising  from  the  surface  diffuse 
themselves  through  it  without  saturating  it. 

After  what  has  just  been  said  of  the  formation  of  mist,  it  will 
easily  be  understood  that  mists  are  especially  formed  in  autumn 
over  rivers  and  lakes,  and  damp  meadows.  In  England,  mists 
are  very  frequent,  from  the  land  being  washed  by  a  warm  sea  ;  in 
like  manner,  the  warm  waters  of  the  Gulf  Stream,  which  flows 
as  far  as  Newfoundland,  are  the  cause  of  the  thick  fogs  met  with 
there. 

We  often  observe  mists  and  fogs  occur  under  totally  different 
circumstances ;  thus  we  find  thick  mists  over  rivers,  whilst  the  air 
is  warmer  than  the  water  or  the  ice.  In  this  case,  the  warm  air 
is  saturated  with  moisture,  and  on  its  mixing  with  the  layers  of 
air,  which  have  acquired  a  lower  temperature  from  being  in  con- 
tact with  the  cold  water  or  ice,  a  condensation  of  the  vapor  is 
necessarily  brought  about. 

The  mists  which  rise  over  rivers  and  lakes  in  summer  after  a 


MISTS    AND    CLOUDS.  597 

storm  of  rain,  originate  in  a  similar  manner.  Although  the  air  is 
warmer  than  the  surface  of  the  water,  it  is  saturated  with  mois- 
ture, and  as  soon  as  it  is  distributed  over  a  place  in  which  the 
freshness  of  the  water  is  perceptible,  the  vapor  becomes  condensed 
by  cooling. 

Mists  are  not,  however,  formed  only  over  rivers  and  lakes,  but 
over  the  middle  of  the  continent,  as  soon  as  the  warmer,  damper 
masses  of  air  are  mixed  with  the  colder,  and  their  temperature 
thus  lowered  below  the  dew  point. 

Clouds  are  nothing  more  than  mists,  which  hover  in  the  higher 
regions  of  the  air,  as  mists  are  nothing  more  than  clouds  resting 
upon  the  surface  of  the  ground.  We  often  see  the  summits  of 
mountains  enveloped  in  clouds,  whilst  persons  upon  these  eleva- 
tions are  in  the  midst  of  mist. 

At  first  sight,  it  appears  incomprehensible  how  clouds  can  float 
in  the  air,  since  they  consist  only  of  vesicles,  which  are  evidently 
heavier  than  the  surrounding  air.  Since  the  weight  of  these 
small  vesicles  of  water  is  very  small  in  comparison  with  their 
surfaces,  the  air  must,  in  this  case,  oppose  a  considerable  resist- 
ance ;  they  can  only  sink  very  slowly,  as  the  soap  bubble,  which 
has  a  great  resemblance  to  these  vesicles  of  vapor,  sinks  but 
slowly  in  a  calm  atmosphere.  These  vesicles  of  vapor  must, 
however,  sink,  although  but  slowly,  and  we  might  thus  suppose 
that,  in  calm  weather,  the  clouds  would,  at  length,  fall  to  the 
ground. 

The  vesicles  of  vapor,  however,  which  sink  in  calm  weather, 
cannot  reach  the  ground,  owing  to  their  soon  reaching  warmer 
strata  of  air  that  are  not  saturated  with  vapor,  and  where  they 
again  dissolve  into  vapor,  and  are  lost  to  view ;  whilst,  however, 
the  vesicles  of  vapor  dissolve  below,  new  ones  are  formed  at  the 
upper  limits,  and  thus  the  cloud  appears  to  float  immovably  in 
the  air. 

We  have  just  considered  vesicles  of  vapor  in  a  perfectly  calm 
atmosphere,  but  when  the  air  is  agitated,  they  must  follow  the 
direction  of  the  current  of  air ;  a  wind  moving  on  in  a  horizontal 
direction,  will  also  carry  the  clouds  with  it  in  the  same  direction, 
and  an  ascending  current  of  air  will  lift  them  up,  as  soon  as  its 
velocity  becomes  greater  than  the  velocity  with  which  these  vesi- 
cles would  fall  to  the  ground  in  a  calm  air.  We  may  also  observe 
how  soap  bubbles  are  carried  away  by  the  wind,  and  borne  over 


598 


MISTS    AND    CLOUDS. 


the  houses.     Thus,  too,  the  rising  of  the  mist  is  explained  by  the 
ascending  currents  of  air. 

The  appearance  of  the  clouds  varies  very  much,  according  as 
they  float  higher  or  lower,  are  more  or  less  dense,  and  are  differ- 
ently illuminated,  &c.  Howard  has  distinguished  clouds  under 
the  following  heads  : — 

1.  The  feathery  cloud-cirrus  consists  of  very  delicate,  more  or 
less  streaked,  open  or  feathery  filaments,  which  first  appear  in  the 
sky  after  fine  weather.     In  our  figure  526,  we  may  observe  these 
in  the  right  hand  corner  towards  the  bottom  where  the  two  birds 
are  hovering.   In  dry  weather,  feathery  clouds  are  more  streaked, 
and  in  damp  weather  more  confused. 

2.  The  dense  cloud,  cumulus,  represented  in  our  figure  exactly 
below  the  feathery  cloud,  forms  large  hemispherical  masses  which 

Fig.  526. 


appear  to  rest  upon  a  horizontal  basis ;  these  clouds  are  of  most 
frequent  occurrence  in  summer,  often  group  themselves  pictur- 
esquely together  in  large  masses,  and  then,  when  lighted  up  by 
the  sun,  present  the  appearance  of  mountains  of  snow. 


STRATIFIED    CLOUDS.  599 

3.  Stratified  clouds,  stratus,  are  horizontal  streaks  of  clouds  ; 
in  our  figure  they  are  represented  below  the  cumulus,  and  appear 
in  extraordinary  brilliancy  of  color  at  sunset. 

The  main  forms  merge  into  a  variety  of  others,  which  Howard 
has  designated  by  the  names  of  cirro-cumulus,  cumulo- stratus,  and 
nimbus. 

The  feathery  accumulated  cloud,  the  cirro-cumulus,  is  the  tran- 
sition of  the  feathery  to  the  dense  cloud ;  they  are  those  small, 
•white,  round  clouds  familiarly  known  as  fleecy. 

When  the  feathery  clouds  are  not  scattered  individually,  but 
combined  in  streaks  of  considerable  extension,  they  form  feathery 
strata  of  clouds,  cirro-stratus,  which  offer  the  appearance  of 
expanded  strata  when  they  are  near  the  horizon  ;  the  cirro-stratus 
often  cover  the  whole  sky  as  with  a  veil. 

When  these  clouds  become  denser,  they  pass  over  into  the 
streaked  accumulated  clouds,  which  often  cover  the  whole  horizon 
with  a  bluish-black  tone  of  color,  and  finally  pass  over  into  the 
actual  rainy  cloud  (nimbus)  depicted  at  the  left  in  our  figure. 

When  we  consider  how  very  various  the  clouds  may  be  in  form 
as  well  as  in  color,  we  shall  easily  understand  how  difficult  it 
often  is  to  decide  whether  the  appearance  of  a  cloud  approaches 
more  to  one  or  other  type. 

The  feathery  clouds  are  the  highest  of  all  kinds  of  clouds, 
since  they  present  the  same  appearance  when  seen  from  high 
hills  as  from  the  valleys  below.  Kdmtz*  determined  their  height 
at  Halle  to  be  about  20,000  feet.  It  is  highly  probable  that  the 
cirrus  does  not  consist  of  vesicles  of  mist,  but  of  flakes  of  snow. 

The  denser  clouds  are  usually  formed  when  the  vapors  are 
raised  up  by  the  ascending  currents  of  air,  and  then  condensed 
by  the  lower  temperature.  Hence,  it  follows,  that  clouds  often 
form  towards  noon,  when  the  sun  has  ascended  in  the  clear  sky ; 
and  towards  evening  the  sky  again  clears,  owing  to  the  sinking  of 
the  clouds  as  the  rising  current  ceases;  the  clouds  again  dissolve 
on  reaching  deeper,  warmer  regions,  if  the  air  be  not  saturated 
with  vapor.  As,  however,  the  south-west  wind  brings  more 
and  more  vapors  with  it  when  the  air  is  saturated  with  vapor, 
the  sinking  clouds  cannot  be  re-dissolved,  but  become  denser  and 
darker,  whilst  a  stratum  of  feathery  clouds  often  floats  above  the 


*  See  «  Complete  Course  of  Meteorology,"  page  365. 


600  QUANTITY    OF    RAIN. 

lower  clouds.  The  lower  masses  of  cloud- cumulus  then  pass 
more  and  more  into  the  cumulo-stratus,  and  rain  maybe  expected. 
When  by  continued  condensation  of  vapor,  the  separate  vesicles 
of  vapor  become  larger  and  heavier,  when  further,  the  separate 
globules  approach  each  other  and  merge  together,  they  form 
actual  drops  of  water,  which  fall  as  rain.  At  a  certain  height  the 
rain-drops  are  still  very  small ;  they  increase  in  size,  however,  as 
they  fall,  owing  to  the  vapor  of  the  strata  of  air  becoming  con- 
densed on  which  account  they  fall. 

Quantity  of  Rain. — The  quantity  of  rain  which  falls  at  anyone 
spot  on  the  earth  in  the  course  of  the  year  is  a  very  important 
element  of  meteorology.  The  instruments  made  use  of  for  this 
purpose  are  termed  Rain  gauges,  Ombrometers  or  Udometers. 
Fig.  527  represents  the  usual  rain  gauge ;  it  consists  of  a  tin 
Fi  527  cylinder  b,  which  is  from  5  to  6  inches  in 

diameter,  and  on  which  a  second  cylinder 
a,  with  a  funnel-like  bottom,  is  placed.  In 
the  centre  of  this  funnel  there  is  an  aper- 
ture; through  which  all  the  water,  falling 
into  the  cylinder  a,  which  is  open  at  the 
top,  flows  into  the  receiver  b.  The  receiver 
6  is  in  connection,  by  means  of  a  curved 
tube  c,  with  a  glass  tube  d,  by  means  of 
which  we  may  every  time  ascertain  how 
high  the  water  stands  in  b.  Provided  that 
the  bores  of  a  and  b  be  equal,  or,  at  any  rate,  not  perceptibly  dif- 
ferent, the  height  of  the  layer  of  water  in  b  indicates  the  height 
to  which  the  ground  would  be  covered  in  a  certain  time,  if  the 
water  were  not  imbibed,  or  evaporated. 

The  annual  quantity  of  rain  is  about  as  follows : 
at  Lisbon  .         .         .25  Paris  inches. 
Dover    .         .         .44         " 
London  .         .23         " 

Paris  .  .  .21  " 
Ratisbon  .  .21  « 
Bergen  .  .  .83  " 
Stockholm  .  .19  " 
Petersburgh  .  .17  " 
Genoa  .  .  .44  " 
Rome  29  « 


QUANTITY    OF    RAIN.  601 

The  quantity  of  rain  that  falls,  is  not,  however,  uniformly  dis- 
tributed throughout  the  year ;  in  this  respect,  Europe  admits  of 
being  divided  into  three  provinces. 

In  England,  on  the  western  coasts  of  France,  in  the  Nether- 
lands, and  in  Norway,  autumnal  rains  predominate. 

In  Germany,  in  the  West-Rhenish  provinces,  Denmark  and 
Sweden,  rains  are  most  prevalent  in  summer. 

Rains  scarcely  ever  fall  during  summer  in  the  south-east  of 
France,  in  Italy,  the  south  of  Portugal,  or  in  that  part  of  Europe 
•which  is  most  contiguous  to  Africa. 

In  Europe,  the  number  of  rainy  days  during  the  year  generally 
decreases  from  south  to  north.  On  the  average  through  the  year 
there  are  about  as  follows : 

in  southern  Europe    .         .     120  rainy  days. 
"  central          "         .         .     146          " 
"  northern       "         .         .     180          " 

That  the  quantity  of  rain  does  not  alone  depend  upon  the 
number  of  rainy  days,  is  evident,  since  it  matters  not  how  many 
days,  but  how  much  it  rains ;  although  the  number  of  rainy  days 
increases  in  northern  districts,  the  intensity  of  the  rain  generally 
diminishes,  and  thus  we  see  why  in  St.  Petersburgh,  for  instance, 
the  number  of  rainy  days  is  in  general  greater,  although  the  quan- 
tity of  rain  that  falls  is  less. 

The  quantity  of  rain,  as  well  as  the  number  of  rainy  days, 
decreases  with  the  increased  distance  from  the  sea ;  thus,  for 
instance,  there  are  about  as  follows : 

iii  St.  Petersburgh          .         .     168 
"  Casan       ....       90 
"  Jakutzk   ....       60 
rainy  days  in  the  course  of  the  year. 

As  under  equal  circumstances  rain  in  warmer  districts  is  more 
intense  than  in  colder,  it  is  also  more  intense  in  the  warmer  than 
in  the  colder  season  of  the  year.     There  are,  on  an  average,  3 
rainy  days  in  Germany  in  the  winter,  and  42  in  the  summer;  the 
number  of  the  rainy  days  in  summer  is,  therefore,  scarcely  more 
considerable  than  in  winter;  and  yet,  the  quantity  of  rain  in 
summer  is  about  double  as  great  as  in  winter.     In  the  summer 
months  there  often  falls  more  rain  in  a  single  storm  than  during 
many  weeks. 
51 


602  RAIN    BETWEEN    THE    TROPICS. 

Rain  between  the  Tropics. — Where  the  trade-winds  blow  with 
the  greatest  regularity,  the  sky  is  for  the  most  part  clear,  and  it 
seldom  rains;  that  is,  when  the  sun  stands  above  the  other 
hemisphere.  On  continents,  however,  the  regularity  of  the  trade- 
winds  is  disturbed  by  the  intensity  of  the  ascending  current  of 
air  as  soon  as  the  sun  approaches  the  zenith ;  about  this  time 
a  violent  rain  sets  in,  which  lasts  many  months,  whilst,  during 
the  remainder  of  the  year,  the  sky  is  uniformly  clear,  and  the 
air  dry. 

Humboldt  has  described  the  phenomena  of  the  rainy  season 
in  the  northern  part  of  South  America.  From  December  till 
February  the  air  is  dry,  and  the  sky  clear.  In  March  the  air 
becomes  more  humid,  the  sky  less  pure ;  the  trade- winds  then 
blow  less  strongly,  and  the  air  is  often  quite  calm.  By  the  end 
of  March,  the  storms  set  in ;  they  begin  in  the  afternoon,  when 
the  heat  is  greatest,  and  are  accompanied  by  violent  torrents  of 
rain.  Towards  the  end  of  April,  the  actual  rainy  season  begins, 
the  sky  is  overcast  with  a  uniform  gray  tint,  and  it  rains  daily 
from  9  A.M.  till  4  P.M.;  at  night  the  sky  is  mostly  clear.  The 
rain  is  the  most  violent  when  the  sun  is  in  the  zenith.  The 
time  during  the  day  in  which  it  rains,  then  becomes  gradually 
shorter,  and  towards  the  end  of  the  rainy  season,  it  rains  only  in 
the  afternoon. 

The  length  of  time  of  the  rainy  season  is  not  the  same  for 
different  districts,  but  lasts,  generally  speaking,  from  3  to  5 
months. 

In  the  East  Indies,  where  the  regularity  of  the  trade-winds  is 
disturbed  by  local  influences,  and  where  the  monsoons  take  their 
place,  we  also  find  irregularities  in  the  quantities  of  rain.  On 
the  steep  western  coasts  of  India,  the  rainy  season  corresponds 
with  our  winter,  occurring  at  the  time  when  the  south-west 
monsoons  prevail,  and,  being  laden  with  humidity,  strike  the 
high  mountains.  Whilst  it  rains  upon  the  coasts  of  Malabar, 
the  sky  is  clear  in  the  eastern  shores  of  Coromandel ;  here  the 
rainy  season  comes  in  with  the  north-east  trade-wind,  that  is, 
exactly  at  the  time  when  the  dry  season  prevails  upon  the  western 
coasts. 

In  the  region  of  calms,  periodical  rains  do  not  prevail;  but  vio- 
lent torrents  of  rain  are  of  almost  daily  occurrence.  The  ascend- 
ing current  of  air  carries  a  mass  of  vapor  on  high,  which  again 


SNOW    AND    HAIL. 


603 


condenses  in  the  colder  regions.  The  sun  almost  always  rises 
with  a  clear  sky,  but  towards  noon  a  few  clouds  are  formed, 
which  become  denser  and  denser,  until,  at  length,  an  immense 
quantity  of  rain  falls,  amid  violent  gusts  of  wind  and  electrical 
discharges.  Towards  evening  the  clouds  disperse,  and  the  sun 
sinks  in  a  clear  sky. 

The  annual  quantity  of  rain  that  falls  in  the  tropics  is,  in 
general,  very  great ;  it  amounts  in  Bombay,  for  instance,  to  73,5, 
in  Candi  to  68,9,  in  Sierra  Leone  to  80,9,  at  Rio  Janeiro  to  55,6, 
at  St.  Domingo  to  100,9,  at  the  Havana  to  85,7,  and  in  Grenada 
to  105  Paris  inches.  If  we  now  consider  that  rain  is  generally 
limited  to  a  few  months,  and  that  it  only  rains  during  a  few 
hours  of  the  day,  it  is  evident  that  the  rain  must  be  very  violent. 
At  Bombay  there  fell,  in  one  day,  6  inches  of  rain,  at  Cayenne 
10  inches  in  10  hours.  The  drops  are  very  large,  and  fall  with 
such  rapidity,  that  they  give  rise  to  a  sensation  of  pain  if  they 
strike  against  the  skin. 

Snow  and  Hail. — Even  at  the  present  time,  we  know  very  little 
regarding  the  formation  of  snow.  It  is  probable  that  the  clouds 
in  which  the  flakes  of  snow  are  first  formed,  consist,  not  of 
vesicles  of  vapor,  but  of  minute  crystals  of  ice,  which,  by  the 
continuous  condensation  of  vapor, 
become  larger,  and  then  form 
flakes  of  snow,  which  continue 
to  increase  in  size  while  falling 
through  the  lower  strata  of  air. 
When  these  lower  regions  are 
too  warm,  the  flakes  of  snow  melt 
before  reaching  the  ground,  so 
that  it  rains  below  while  it  snows 
above. 

The  regular  form  assumed 
by  flakes  of  snow,  in  the  state 
which  they  can  be  best  observed, 
namely,  when  they  are  placed  on 
a  dark  body  cooled  below  32°, 
was  first  described  by  Kepler. 
Scoresby  had  an  opportunity,  in 
the  polar  regions,  of  making  a 
number  of  interesting  observa- 


Fig.  528. 


604  SNOW    AND    HAIL. 

lions  on  the  forms  of  the  flakes.  His  work  contains  nearly  100 
different  plates,  of  which  some  of  the  most  interesting  have  been 
collected  in  Fig.  528. 

A  mere  superficial  glance  at  these  figures  shows  that  all  their 
forms  are  essentially  referable  to  a  regular  hexagonal  star,  from 
whence  it  follows  that  snow-flakes  belong  to  the  hexagonal  sys- 
tem of  crystals  (the  crystal-system  of  rock  crystals). 

Sleet,  which  we  usually  observe  in  March  and  April,  is  formed 
in  the  same  manner  as  snow.  The  granules  of  sleet  are  formed 
of  tolerably  firm  spherical  icicles. 

Hail  is  one  of  the  most  fearful  scourges  to  the  agriculturist,  and 
one  of  the  most  mysterious  phenomena  to  the  meteorologist. 

The  ordinary  size  of  hail-stones  is  that  of  a  hazel-nut;  they  are 
very  frequently  smaller ;  but  these,  being  less  dangerous,  are  not 
particularly  regarded.  They  are  often,  however,  much  larger, 
and  destroy  everything  they  strike. 

Trustworthy  philosophers  have  observed  hail-stones  which 
weighed  12  to  13  ounces. 

The  form  of  hail-stones  is  liable  to  great  variation ;  most  com- 
monly they  are  rounded,  but  sometimes  flattened  and  angular. 
In  their  centre  there  is  usually  an  opaque  nucleus,  resembling  a 
granule  of  sleet:  this  nucleus  is  surrounded  by  a  transparent  mass 
of  ice,  in  which  we  may  often  observe  separate  concentric  layers ; 
sometimes  alternating  layers  of  transparent  and  opaque  ice  may 
be  seen ;  and,  finally,  even  hail-stones  with  a  striated  structure 
have  been  observed. 

Pouillet  found  that  the  temperature  of  hail-stones  varied  from 
31  to  25°. 

Hail  generally  precedes  a  thunder-storm.  It  never,  or  at  any 
rate,  but  very  rarely,  follows  rain ;  at  least,  when  the  latter  has 
continued  some  time. 

A  hail-storm  generally  lasts  only  a  few  minutes,  very  seldom 
so  long  as  a  quarter  of  an  hour.  The  quantity  of  ice  which 
escapes,  from  the  clouds  in  so  short  a  time  is  enormous ;  the  earth 
being  often  covered  by  it  to  the  depth  of  several  inches. 

Hail  falls  more  frequently  by  day  than  by  night.  The  clouds 
which  bring  it  seem  to  have  a  considerable  extension  and  depth, 
for  they  generally  occasion  great  darkness.  It  is  believed  that 
they  have  been  seen  of  a  peculiar  grayish  red  tint,  and  that  great 


SNOW    AND    HAIL.  605 

masses  of  clouds  were  suspended  from  their  lower  confines,  and 
their  edges  variously  indented. 

Hail-clouds  seem  generally  to  float  very  low.  The  inhabitants 
of  mountainous  districts  often  see  clouds  below  them,  which  cover 
the  valleys  with  hail ;  it  cannot,  however,  be  determined  with 
accuracy  whether  hail-clouds  always  descend  so  low. 

A  peculiar  rustling  noise  is  heard  a  few  seconds  before  the 
beginning  of  a  hail-storm;  and,  finally,  hail  is  always  accom- 
panied by  electrical  phenomena. 

As  to  what  concerns  the  explanation  of  hail,  this  presents  two 
difficulties :  namely,  as  to  whence  the  great  cold  comes,  which 
causes  the  water  to  freeze  ;  and  next,  how  it  is  possible  that  the 
hail-stones,  after  having  once  become  large  enough  to  fall  by  their 
own  weight,  can  yet  remain  long  enough  in  the  air  to  increase  to 
so  considerable  a  size. 

With  regard  to  the  first  question,  Volta  thought  that  the  solar 
rays  were  almost  wholly  absorbed  at  the  upper  confines  of  the 
dense  clouds,  which  would  necessarily  occasion  a  rapid  evapora- 
tion, especially  when  the  air  above  the  clouds  was  very  dry;  this 
evaporation  would,  according  to  him,  cause  so  much  heat  to  be 
absorbed,  that  the  water  in  the  lower  strata  of  air  would  freeze. 
If,  however,  the  evaporation  of  the  water  in  the  upper  stratum  of 
air  were  occasioned  by  the  heat  of  the  solar  rays,  it  is  not  so  clear 
why  so  much  heat  should  be  withdrawn  from  the  lower  layers  of 
clouds  by  means  of  this  evaporation. 

With  reference  to  the  second  question  Volta  proposed  a  very 
ingenious  theory,  which  has  attained  great  celebrity.  He  assumes 
that  two  layers  of  clouds,  heavily  charged  with  opposite  kinds  of 
electricity^  hover  above  one  another.  If,  now,  the  very  small  hail- 
stones fall  upon  the  lower  clouds,  they  will  penetrate  to  a  certain 
depth,  and  thus  become  surrounded  by  a  new  layer  of  ice ;  they 
will,  however,  also  become  charged  with  the  electricity  of  the 
lower  cloud,  and  be  repelled  by  it,  while  they  will  be  attracted 
by  the  other ;  they  will,  therefore,  again  rise,  in  spite  of  their 
gravity,  to  the  upper  cloud,  where  the  same  process  will  be  re- 
peated ;  thus  they  will  move  for  a  time  backwards  and  forwards 
between  the  two  clouds,  until  at  last  they  will  fall,  when  they 
become  heavy  enough,  and  when  the  clouds  have  lost  their  elec- 
tricity. 

51* 


(506  COLOR   OF    THE    SKY. 

It  may  be  objected  to  this  view,  that  it  is  scarcely  conceivable 
that  electricity  is  able,  without  any  sudden  action,  that  is,  with- 
out any  explosive  discharge,  to  raise  such  large  masses  of  ice ; 
and  that  if  the  electric  charge  of  the  two  clouds  were  really  so 
powerful,  the  electricity  must  instantaneously  pass  from  one  to 
the  other;  especially  since  the  hail-stones  must  establish  a  con- 
nection between  them. 


CHAPTER    IV. 

OPTICAL  PHENOMENA  OF  THE  ATMOSPHERE. 

Color  of  the  Sky. — The  clear  sky  appears  to  us  to  be  blue,  and 
this  blue  is  sometimes  brighter  and  whiter,  and  sometimes  darker, 
according  to  the  state  of  the  atmosphere  ;  on  high  mountains  the 
sky  appears  dark  blue,  or  almost  black.  This  is  readily  explained : 
if  the  air  were  perfectly  transparenf,  if  its  individual  particles 
reflected,  or  rather  scattered  no  light,  the  sun,  moon  and  stars 
would  shine  out  forth  from  a  black  ground ;  but,  as  it  actually  is, 
the  particles  of  air  reflect  the  light,  and  thus  it  happens  that  during 
the  day  the  whole  sky  appears  bright,  because  the  particles  of  air 
illuminated  by  the  sun  scatter  the  light  in  all  directions.  This 
illumination  of  the  atmosphere  by  the  sun's  rays  is  the  cause  of 
our  not  seeing  the  stars  during  the  day.  The  particles  of  air 
reflect  mostly  blue  light,  and  hence  it  is  that  the  dark  vault  of 
heaven  is  invested  with  a  blue  tint.  The  higher  we  rise  in  the 
atmosphere,  so  much  the  thinner  is  the  blue  envelop,  and  conse- 
quently so  much  the  darker  does  the  heaven  above  us  appear ;  thus 
the  darkest  blue  is  always  in  the  zenith,  while  towards  the  hori- 
zon there  is  more  of  a  whitish  tint. 

The  pure  blue  of  the  sky  is  especially  decolorized  by  the  con- 
densed vapor  floating  in  the  air,  by  fine  mists,  which  often  invest 
the  sky  as  with  a  delicate  veil,  without  being  sufficiently  dense  to 
appear  as  clouds. 

The  phenomena  of  the  evening  and  morning  red  are  explained 
by  saying  that  the  air  permits  of  the  passage  of  the  red  and  yel- 
low rays  in  preference,  but  that  it  reflects  the  blue  rays.  The 


COLOR   OF    THE    SKY.  607 

sun's  rays  in  the  evening  and  morning  have  to  traverse  a  con- 
siderable space  through  the  atmosphere,  hence  the  red  coloring 
of  the  transmitted  rays,  which  is  particularly  brilliant  when  clouds 
are  illuminated  by  them. 

This  opinion  cannot  be  altogether  correct,  because  the  blue 
tint  of  the  sky  is  not  the  complementary  color  of  the  evening  red. 
The  evening  red  depends  probably  on  the  vapor  of  water  con- 
tained in  the  air. 

When  a  column  of  steam  rises  from  the  safety-valve  of  a  steam- 
engine,  as,  for  instance,  of  a  locomotive,  the  sun  seen  through 
the  steam  appears  of  a  deep  orange  red ;  some  feet  above  the 
safety-valve,  at  which  the  steam  is  escaping,  its  color  by  trans- 
mitted light  has  the  deep  orange  tint  already  described ;  at  a 
greater  distance,  where  the  vapor  is  more  perfectly  condensed,  the 
phenomenon  entirely  disappears.  Even  a  moderately  thick  cloud 
of  vapor  is  perfectly  impenetrable  to  the  sun's  rays  ;  it  throws  a 
shadow  like  a  solid  body ;  and  when  its  thickness  is  small,  it  is 
then  indeed  transparent,  but  colorless  throughout.  The  orange 
color  of  vapor  appears,  therefore,  to  pertain  to  a  peculiar  state  of 
condensation.  In  a  perfectly  gaseous  state,  aqueous  vapor  is 
quite  transparent  and  colorless ;  in  any  transitive  state,  it  is  trans- 
parent and  of  a  dingy  red  ;  but  when  it  is  perfectly  condensed 
into  vesicles  of  mist,  a  thin  layer  is  transparent  and  colorless, 
while  a  thick  layer  is  perfectly  opaque. 

Aqueous  vapor,  being  a  pure,  colorless,  elastic  fluid,  gives  to 
the  air  most  of  its  transparency,  particularly  as  is  observed  when 
the  sky  clears  after  a  severe  rain.  In  the  transition  stage,  it  ad- 
mits of  the  passage  of  the  yellow  and  red  rays,  and  in  this  con- 
dition gives  rise  to  the  appearance  of  the  evening  red. 

This  theory  will  also  explain  why  it  is  that  the  evening  red  is 
far  more  brilliant  than  the  morning  red;  that  the  evening  red  and 
the  morning  gray  are  signs  of  fine  weather.  Immediately  after 
the  maximum  diurnal  temperature  has  been  attained,  and  before 
sunset,  the  surface  of  the  earth  and  strata  of  air  at  different  heights 
begin  to  lose  heat  by  radiation.  Before,  however,  this  has  led  to 
the  entire  condensation  of  the  aqueous  vapor,  it  passes  through 
that  transition  stage  which  causes  the  evening  red.  In  the  morn- 
ing the  case  is  different.  The  vapors  which,  in  the  reversion  of 
the  process,  would  probably  have  given  rise  to  the  red,  do  not  rise 
till  they  have  been  exposed  sufficiently  long  to  the  sun's  action; 


608  THE  RAINBOW. 

but  then  the  time  of  the  sun's  rising  is  over,  and  the  sun  stands 
high  in  the  heavens.  The  fiery  appearance  of  the  morning  sky 
depends  on  the  presence  of  such  an  excess  of  moisture,  that  by 
its  condensation  in  the  higher  regions,  actual  clouds  are  formed, 
notwithstanding  the  tendency  of  the  rising  sun  to  disperse  them ; 
the  morning  red  is,  therefore,  to  be  considered  as  the  forerunner 
of  speedy  rain. 

When  the  sun  has  disappeared  in  the  western  horizon,  instead 
of  there  being  immediate  darkness,  we  have  the  twilight,  which 
lasts,  under  different  circumstances,  for  a  longer  or  shorter  time. 
The  twilight  is  produced  by  the  sun's  continuing  to  shine  on  the 
atmosphere  of  the  western  sky,  and  on  the  aqueous  particles  sus- 
pended in  it,  for  some  time  after  it  has  disappeared  from  our 
view,  and  on  these  illuminated  particles  of  air  and  water  con- 
tinuing to  transmit  to  us  a  light  which  becomes  gradually  fainter 
and  fainter.  In  Germany,  and  countries  of  the  same  latitude,  the 
twilight  lasts  till  the  sun  is  about  18°  beltfw  the  horizon.  The 
prolonged  duration  of  twilight  in  higher  latitudes  is  dependent  on 
the  circumstance  that  the  sun's  orbit  is  there  very  strongly  in- 
clined towards  the  horizon,  and  that,  consequently,  it  takes  a  very 
considerable  time  for  the  sun  to  sink  18°  below  it.  The  nearer 
we  approach  to  the  equator,  so  much  the  less  oblique  is  the  sun's 
orbit  towards  the  horizon,  until  under  the  equator  the  two  are  at 
right  angles ;  in  hot  countries  the  twilight  is,  therefore,  of  shorter 
duration.  In  Italy  it  is  shorter  than  in  Germany,  in  Chili  it  lasts 
only  a  quarter  of  an  hour,  and  in  Cumana  only  a  few  minutes. 
This  extremely  short  twilight  is  not  solely  to  be  referred  to  the 
direction  of  the  sun's  orbit  with  respect  to  the  horizon;  we  must 
also  take  into  consideration  the  extraordinary  purity  of  the  sky  in 
those  countries,  for  in  our  regions  the  delicate  mists  which  float 
high  in  the  air,  and  during  the  day,  veil  the  sky,  materially  assist 
in  reflecting  the  light,  and  so  prolonging  the  twilight. 

The  Rainbow. — Every  one  knows  that  we  see  a  rainbow  when  we 
have  the  sun  behind  us,  and  face  a  showery  cloud.  The  rainbow 
forms  the' base  of  a  cone,  whose  vertex  is  the  eye,  and  whose  axis 
coincides  with  the  straight  line  passing  through  the  sun  and  the 
eye.  Under  the  above  conditions  the  rainbow  appears  in  the  mist 
of  waterfalls  and  fountains. 

In  order  to  explain  the  formation  of  the  rainbow,  we  must  follow 
the  course  of  the  sun's  rays  through  a  drop  of  rain. 


THE    RAINBOW. 


609 


Fig.  529. 


If  a  ray  SA  (Fig.  529)  strikes  a  rain-drop,  it  is  refracted,  and  it 
is  easy  to  calculate  or  to  con- 
struct the  direction  of  the  re- 
fracted ray  Ji  B.  The  refracted 
ray  Jl  B  is  reflected  at  .B,  by 
the  posterior  wall  of  the  drop 
to  C,  and  then  after  a  second 
refraction  emerges  in  the  direc- 
tion C  0.  The  emergent  ray 
C  0  forms  with  the  incident 
ray  an  angle  S  JV*  0. 

But  many  other  rays  fall  on 
the  drop  parallel  with  SA\  and  if  we  calculate  or  construct  for 
each  of  them  their  path  through  the  drop,  as  we  have  done  in  the 
figure  for  a  second  ray,  it  will  be  found  that  the  emergent  rays  are 
not  parallel  to  one  another. 

While,  therefore,  a  parallel  pencil  of  light  falls  on  the  drop,  a 
pencil  of  light  strongly  divergent  emerges  from  it.  It  is  easy  to 
understand,  that  by  this  divergence  of  the  rays  emerging  from  the 
drop,  the  strength  of  the  impression  of  the  light  which  they  produce 
is  very  much  weakened,  especially  when  the  drops  occur  at  only 
a  slight  distance  from  the  eye.  Of  all  the  rays  which  enter  the  eye 
from  a  drop  after  two  refractions  and  one  reflection,  those  only  can 
make  that  perceptible  impression  of  light  for  which  the  divergence 
is  a  minimum,  or,  in  other  words,  only  those  which  emerge  very 
nearly  parallel. 

From  more  accurate  examination,  it  follows  that  a  considerable 
number  of  parallel  incident  rays  fall  or  leave  the  drop  nearly  in 
the  same  direction,  having  suffered  a  deviation  of  very  nearly  42° 
30';  and  of  all  the  rays  emerging  from  the  drop,  these  alone  can 
produce  a  sensible  impression  of  light. 

Let  us  suppose  a  straight  line  o  p  (Fig.  530)  to  be  drawn 
through  the  sun  and  the  eye  of  the  observer,  and  a  vertical  plane 
to  be  carried  through  it.  If  through  o  we  draw  the  straight  line 
o  v,  so  that  the  angle  p  o  v  =  42°  30',  then  the  rain-drops  in  this 
direction  will  send  effective  rays  to  the  eye  after  an  internal  re- 
flection. The  eye,  however,  does  not  receive  effective  rays  from 
this  direction  alone,  but,  as  may  easily  be  conceived,  likewise 
from  all  the  drops  of  rain  which  lie  on  the  surface  of  the  cone, 
which  arises  from  the  revolution  of  the  line  o  v  about  the  axis  op. 


610 


THE    RAINBOW. 


the  eye  will,  therefore,  see  a  circle  of  light,  the  central  point  of 
which  lies  upon  the  straight  line  drawn  through  the  eye,  and 
whose  radius  appears  under  an  angle  of  42°  30'. 

Fig.  530. 


In  the  direction  mentioned  we  observe  a  circle,  which  appears 
as  a  red  ring,  about  30'  in  breadth,  in  consequence  of  the  sun 
not  being  a  mere  point,  but  a  disc,  whose  apparent  diameter  is 
30'.  But  as  the  effective  violet  rays  emerge  in  a  direction  mak- 
ing an  angle  of  40°  30'  with  the  incident  rays,  the  eye  per- 
ceives a  violet  ring  about  30'  broad,  whose  radius  amounts  to 
only  40°  30'.  Between  these  external  arcs  we  observe  the  other 
prismatic  colors,  and  thus  the  rainbow  forms,  as  it  were,  a  spec- 
trum extended  into  a  circular  arc.  The  whole  breadth  of  the 
rainbow  averages  2°,  since  the  radius  of  the  red  bow  is  2° 
greater  than  that  of  the  violet. 

The  extension  of  the  colored  arc  obviously  depends  on  the 
sun's  altitude  above  the  horizon.  When  the  sun  is  fast  going 
down,  the  rainbow  appears  in  the  east,  the  centre  of  the  bow 
then  lying  exactly  in  the  horizon,  since  the  line  drawn  through 
the  sun  and  the  eye  is  then  a  horizontal  line ;  when  the  observer 
stands  on  a  plane,  the  rainbow  then  forms  an  exact  semicircle; 
he  can,  however,  see  more  than  a  semicircle,  if  he  stand  on  an 
isolated  mountain-top  of  small  breadth.  At  sun-rise  the  rainbow 
appears  in  the  west.  In  proportion  to  the  height  of  the  sun,  so 


THE    RAINBOW.  61 1 

much  the  lower  is  the  centre  of  the  colored  bow  below  the  hori- 
zon, and,  consequently,  so  much  the  smaller  is  the  portion  of  the 
bow  visible  to  the  eye.  If  the  sun's  elevation  above  the  hori- 
zon is  42°  30',  no  rainbow  is  any  longer  visible  to  an  observer 
standing  on  a  plane  at  the  level  of  the  sea,  since  then  its  summit 
coincides  with  the  horizon,  and  the  whole  arc  falls  below  it. 
From  the  masts  of  ships  we  often  observe  rainbows  forming  a 
perfect  circle.  Such  circular  rainbows  are  also  often  observed 
in  waterfalls  and  fountains. 

Besides  the  rainbow  already  described,  we  also  usually  observe 
a  second  and  larger  one,  concentric  with  the  first,  but  having 
the  order  of  the  colors  reversed,  in  the  exterior  rainbow  the  red 
being  the  inner,  and  the  violet  the  exterior  color.  The  external 
rainbow  is  much  the  paler  of  the  two,  and  has  the  colors  much 
less  strongly  developed.  Formerly  it  was  erroneously  believed 
that  the  second  rainbow  was  a  mere  image  of  the  first.  The 
formation  of  the  outer  bow  depends  on  exactly  the  same  princi- 
ples as  that  of  the  inner  bow,  and  is  produced  by  the  sun's  rays, 
which  have  undergone  a  second  refraction  and  a  second  internal 
reflection  in  the  rain-drops. 

In  Fig.  531  is  represented  the  course  which  a  ray  of  light 
pursues  in  the  rain-drop  in  order  to 

be  a  second  time  reflected.     S  A  is        lg'° 

the  incident  ray,  which  is  refracted 
in  the  direction  Jl  jB,  then  reflected 
at  B  and  C,  and,  finally,  refracted 
at  D  in  the  direction  D  0.  In  this 
case  the  incident  and  the  emergent 
rays  intersect,  forming  with  one 
another  an  angle  d,  whose  magni- 
tude varies  according  as  the  inci- 
dent ray  impinges  on  the  drop  at  another  place,  therefore  under 
another  angle  of  incidence. 

In  this  case  the  effective  emergent  red  rays  form  an  angle  of 
50°,  and  the  effective  emergent  violet  rays  an  angle  of  53J°  with 
the  incident  rays ;  the  eye,  therefore,  perceives  a  series  of  con- 
centric colored  rings,  the  innermost  of  which  is  red,  and  has  a 
radius  of  50°,  whilst  the  outermost  one,  the  violet,  has  a  radius 
of  53£°. 

The  outer  rainbow  is  the  paler  because  it  is  formed  by  rays 


612 


HALOS    AND    PARHELIA. 


which  have  undergone  a  second  internal  reflection,  and  (as  is 
well  known)  after  every  reflection  light  becomes  weaker.  We 
should  be  able  to  see  a  third,  and  even  a  fourth  rainbow,  formed 
by  rays  which  had  undergone  three  or  four  internal  reflections,  if 
the  light  of  these  rays  were  not  too  faint. 

Halos  and  Parhelia. — When  the  sky  is  invested  with  light 
clouds,  we  often  observe  colored  rings  close  round  the  sun  and 
moon.  These  rings  are  frequently  imperfect,  and  mere  portions. 
The  fact  that  lunar  halos  are  more  frequently  observed  than  solar 
halos,  is  dependent  on  the  circumstance  that  the  sun's  light  is 
too  dazzling;  the  latter  are,  however,  seen  on  observing  the  sun's 
image  in  still  water,  or  in  a  mirror  blackened  at  the  back. 

These  halos  present  the  greatest  similarity  to  the  glory  ob- 
servable round  the  flame  of  a  taper  on  looking  at  it  through  a 
glass  plate  on  which  lycopodium  seed  has  been  strewed;  in  fact, 
both  these  phenomena  depend  on  the  phenomena  of  interference ; 
the  vesicles  of  vapor  may  replace  the  minute  particles  of  seed  in 
the  latter  case. 

Fig.  532. 


Sometimes  we  also  notice  two  larger  colored  circles  around 
the  sun  and  moon ;  these  must  not  be  mistaken  for  halos.  The 
radius  of  the  smaller  of  these  luminous  rings  appears  under  an 


IGNIS   FATUUS.  613 

angle  of  22°  or  23°,  whilst  that  of  the  greater  under  an  angle  of 
46°  or  47°.  The  red  in  them  is  inverted  inward ;  the  inner  edge 
is  the  sharper,  the  outer  is  more  undefined  and  less  decidedly 
colored.  The  two  circles  rarely  appear  simultaneously.  Fig. 
532  exhibits  the  phenomenon  as  we  have  most  commonly  the 
opportunity  of  observing  it ;  the  smaller  ring  has  a  radius  of  22° 
or  23° ;  it  is  intersected  by  a  horizontal  streak  of  light,  which 
often  extends  to  the  sun  itself.  The  streak  is  brightest  at  the 
points  where  it  intersects  the  ring  of  light ;  these  bright  spots, 
which  we  observe  on  both  sides  of  the  sun  on  the  outer  circum- 
ference of  the  ring,  are  the  parhelia;  sometimes  one  such  parhe- 
lion appears  vertically  above  the  sun  at  the  summit  of  the  ring ;  but 
at  this  point,  also,  there  is  often  seen  an  arc  of  contact,  as  shown 
in  Fig.  532.  Moreover,  we  often  observe  parhelia  without  rings, 
or  rings  without  parhelia.  These  rings  and  parhelia  never  appear 
in  a  perfectly  unclouded  sky,  but  only  when  it  is  overcast. 

The  appearance  of  these  rings  has  been  explained  by  assuming 
that  light  is  refracted  by  the  crystals  of  ice  suspended  in  the  atmo- 
sphere. If  the  icicles  are  six-sided  prisms,  the  two  non-parallel 
and  non-joining  sides  always  form  with  one  another  an  angle  of 
60°;  the  icicles  form,  therefore,  regular,  equilateral,  triangular 
prisms,  in  which  the  minimum  of  deviation  is  about  23°.  Rays, 
which  have  undergone  in  the  icicles  the  minimum  of  deviation, 
are  analogous  to  the  active  rays  in  the  rainbow,  since  many  rays 
emerge  very  nearly  in  the  same  direction.  This  hypothesis,  there- 
fore, explains  at  the  same  time  the  formation  of  the  ring,  its  size, 
and  the  order  in  which  the  colors  take  place. 

The  ring  of  46°  is  explained  by  the  assumption  that  the  axis 
of  the  prisms  stands  obliquely,  in  such  a  manner  that  the  right 
angle  which  the  lateral  surfaces  of  the  prism  make  with  the  base 
is  the  refracting  angle  of  the  prism.  For  a  prism  of  ice,  whose 
refracting  angle  is  90°,  the  minimum  of  deviation  is,  in  point  of 
fact,  46°. 

The  light  streaks  accompanying  the  parhelia  are  explained  by 
the  reflection  of  the  sun's  rays  from  the  vertical  surfaces  of  the 
crystals  of  ice.  The  streak  is  brightest  where  it  cuts  the  ring  of 
23°,  since  here  two  causes  co-operate  to  affect  the  stronger  illu- 
mination. 

Ignis  Fatuus,  or  the  Will-o> -the- Wisp,  is  the  name  usually 
given  to  certain  flames  seen  in  marshy  lands,  moors,  churchyards, 


614          FALLING    STARS,    FIRE-BALLS,    AND   AEROLITES. 

&c.,  in  fact,  wherever  putrefaction  and  decomposition  are  going 
on ;  they  usually  appear  a  little  above  the  ground,  exhibit  a  flick- 
ering and  unsteady  motion,  and  soon  again  vanish.  Although 
we  are  usually  in  the  habit  of  treating  these  lights  as  thoroughly 
understood  phenomena,  there  is  yet  great  uncertainty  regarding 
them,  since  they  have  not  been  sufficiently  explained,  and  what  is 
considered  as  matter  of  fact  not  at  all  times  to  be  received,  owing 
to  the  circumstance  that  most  persons  who  have  seen  them  were 
not  in  a  state  to  make  accurate  observations,  and  to  explain  in  an 
unprejudiced  manner  what  they  saw. 

Volta  held  the  opinion  that  these  lights  were  caused  by  marsh 
gas  (light  carburetted  hydrogen)  inflamed  by  an  electric  spark. 
But  from  whence  could  the  spark  arise  ?  Others  are  of  opinion 
that  they  are  caused  by  phosphuretted  hydrogen,  which  inflames 
as  soon  as  it  comes  into  contact  with  atmospheric  air ;  but  then 
there  would  be  a  momentary  flash  accompanied  by  a  puff  of 
smoke,  and  not  a  prolonged  feeble  light,  such  as  is  observed. 
The  most  probable  view  is,  that  they  are  caused  by  hydrogen  gas 
containing  phosphorus,  which  does  not,  properly  speaking,  burn 
as  a  flame,  but  is  only  faintly  pbosphorescent. 

Falling  Stars,  Fire-balls,  and  Meteoric  Stones. — The  appearance 
presented  by  falling  stars  is  so  generally  known  as  to  require 
no  detailed  description.  It  has  been  ascertained  by  corresponding 
observations  that  the  height  of  falling  stars  averages  34  or  35 
(German)  miles,  and  that  they  move  with  a  velocity  varying  from 
4  to  8  (German)  miles  in  a  second. 

A  very  remarkable  phenomenon  connected  with  falling  stars,  is 
the  periodically  recurring  showers,  which  have  been  observed 
from  the  12th  to  the  14th  of  November,  and  on  the  10th  of  August 
(the  Feast  of  St.  Lawrence) ;  these  periodic  showers  of  stars  of 
the  latter  date  are  noticed  in  an  ancient  English  church  calendar, 
and  are  termed  the  fiery  tears  of  the  Saint.  One  of  the  most 
considerable  of  these  showers  of  stars  was  observed  in  North 
America  on  the  12th  and  13th  of  November,  1833;  they  appeared 
to  fall  almost  in  contact,  like  flakes  of  snow  in  a  snow-storm,  and 
it  was  calculated,  that  in  the  course  of  nine  hours  no  less  than 
240,000  fell. 

Fire-balls  appear  to  have  the  same  origin,  and  to  be  of  the 
same  nature  as  the  falling  stars  just  described,  and  to  differ  from 


FALLING   STARS,    FIRE-BALLS,   AND   AEROLITES.         615 

them  merely  in  size.     Fire-balls  have  been  seen  amongst  the 
great  falling  stars. 

Fire-balls  explode  with  a  great  noise,  and  stony  masses  then 
fall  from  them,  known  as  meteoric  stones,  or  aerolites.  Even 
during  the  day-time  such  meteoric  stones  have  been  seen  to  fall, 
with  a  loud  report,  from  small  gray  clouds. 

Meteoric  stones,  just  fallen,  are  still  hot,  and  in  consequence 
of  the  velocity  of  their  fall,  penetrate  the  earth  to  a  greater  or 
less  degree. 

About  the  era  of  the  last  century,  there  was  a  strong  tendency 
to  regard  the  falling  of  stony  masses  from  the  atmosphere  as 
fabulous  ;  but  since  that  period  various  cases  have  occurred,  which 
have  been  observed  by  several  persons,  and  have  been  attested  to 
by  men,  in  whom  confidence  must  be  placed.  We  may  especially 
mention  the  meteoric  stone  that  fell  at  Aigle,  in  the  department  of 
Orne,  on  the  26th  of  April,  1803,  examined  by  Biot,  and  that  on 
the  22d  of  May,  1808,  and  that  at  Stauners,  in  Moravia.  On 
the  13th  of  November,  1835,  (at  the  period,  therefore,  of  the  fall- 
ing stars,)  a  house  in  the  department  of  Ain  was  set  on  fire  by 
an  aerolite. 

Meteoric  stones  have  a  peculiar  physiognomy,  by  which  they 
may  be  distinguished  from  all  terrestrial  fossils ;  but  notwith- 
standing this,  they  differ  so  much  individually,  that  Chladni,  who 
devoted  much  attention  to  these  subjects,  regarded  it  as  difficult 
to  assign  to  them  a  general  character.  One  of  their  most  marked 
characteristics  is,  however,  their  containing  a  certain  amount  of 
native  iron,  and  a  bituminous,  glistening,  sometimes  raised  ex- 
ternal crust,  which  is  scarcely  ever  absent.  A  further  descrip- 
tion would  involve  us  too  deeply  in  mineralogical  details. 

Stony  masses  have  been  found  at  various  spots  on  the  earth's 
surface,  perfectly  distinct  in  geological  character  from  the  moun- 
lin  range  in  the  vicinity,  but  presenting  the  greatest  similarity  to 

mes  known  to  be  of  meteoric  origin.  Hence  such  masses  are 
considered  to  be  aerolites. 

The  mass  of  meteoric  stones  is  often  very  great;  they  have 

?en  found  weighing  from  a  few  pounds  up  to  400  cwt. 

It  can  hardly  be  longer  doubted  that  falling  stars,  fire-balls, 
md  meteoric  stones,  are  of  cosmical  origin,  or  that  they  are  most 
>robably  masses  which,  like  the  planets,  revolve  round  the  sun, 
1  id,  being  drawn  within  the  sphere  of  the  earth's  attraction, 


616  DISCOVERY    OF   ATMOSPHERIC    ELECTRICITY. 

fall.  The  fire  and  light  accompanying  them,  are  most  easily 
accounted  for  by  the  assumption  that  these  minute  spheres  are 
surrounded  with  an  atmosphere  of  inflammable  gas,  which  in- 
flames on  entering  into  the  oxygenized  atmosphere  of  our  earth. 
If  we  assume  that,  besides  the  innumerable  individual  masses  of 
this  kind  revolving  round  the  sun,  whole  swarms  of  them  form 
a  ring  round  that  body,  and  further,  that  the  plane  of  this  ring 
cuts  the  earth's  orbit  at  a  definite  point,  we  have  an  explanation 
of  showers  of  the  periodic  falling  stars. 


CHAPTER    V. 

ON  ATMOSPHERIC  ELECTRICITY. 

Original  Discovery  of  Jltmo  spheric  Electricity. —  Otto  von  Gue- 
rike,  the  distinguished  inventor  of  the  air-pump,  was  the  first  who 
observed  an  electric  appearance  of  light.  About  the  same  time, 
Wall  noticed  a  vivid  spark,  and  heard  a  strong  rustling  sound, 
on  rubbing  a  large  cylinder  of  resin,  and  it  is  a  remarkable  thing 
that  the  first  sparks  drawn  by  the  human  hand  were  compared  to 
lightning.  These  sparks,  and  these  cracks  seemed,  says  Wall,  to 
a  certain  degree,  to  represent  thunder  and  lightning.  The 
analogy  was  surprising ;  in  order,  however,  to  test  its  truth, 
and  to  detect,  in  so  minute  an  appearance,  the  causes  and  laws  of 
one  of  the  grandest  phenomena  of  nature,  it  was  requisite  that 
there  should  be  a  more  direct  proof.  Whilst  in  Europe  men 
occasionally  asserted  that  lightning  was  actually  an  electric  phe- 
nomenon, its  experimental  proof  was  established  in  America. 
Franklin,  after  making  many  electrical  discoveries,  especially  on 
the  Leyden  jar,  and  on  the  influence  of  points,  arrived  at  the 
happy  idea  of  searching  for  electricity  even  in  thunder  clouds; 
he  concluded  that  metallic  points,  placed  on  lofty  buildings,  would 
draw  off  the  electricity  from  the  clouds.  He  waited  with  im- 
patience for  the  completion  of  a  steeple  then  being  constructed  in 
Philadelphia ;  but  at  length,  weary  of  waiting,  he  had  recourse  to 
another  plan,  which  gave  him  even  more  certain  results.  Since 


ELECTRICITY   DURING   A   THUNDER   STORM.  617 

all  that  was  requisite  was  to  raise  a  body  a  sufficient  height  in  the 
air,  he  conceived  that  a  kite,  a  child's  toy,  would  answer  his  pur- 
pose as  well  as  the  highest  steeple.  He  availed  himself  of  the 
first  thunder-storm,  in  order  to  try  his  experiment ;  accompanied 
by  a  single  person,  his  own  son,  since  he  was  afraid  of  ridicule 
if  his  attempt  failed,  he  set  off  into  the  open  country,  and  began 
to  fly  his  kite.  A  cloud  of  great  promise  passed  over  them  with- 
out producing  the  least  action.  Another  passed  over,  but  he 
could  draw  no  sparks,  nor  could  he  see  any  signs  of  electricity. 
At  length  the  fibres  of  the  string  began  to  separate  from  one  an- 
other, and  he  heard  a  rustling  noise.  Encouraged  by  these  signs, 
Franklin  applied  his  finger  close  to  the  end  of  the  string,  and 
then  observed  the  emission  of  a  spark,  which  was  quickly  followed 
by  many  others. 

Franklin  performed  his  experiment  in  June,  1752 ;  it  was  uni- 
versally repeated  with  the  same  results.  De  Romas,  at  Nerac, 
influenced  by  the  first  idea  of  Franklin,  had  likewise  thought  of 
making  use  of  a  kite  instead  of  elevated  points.  Without  having 
received  any  account  of  the  results  arrived  at  by  Franklin,  he 
obtained  in  June,  1753,  very  powerful  evidences  of  electricity, 
owing  to  his  ingenious  contrivance  of  laying  a  fine  metal  wire  the 
whole  length  of  the  string.  In  the  year  1757,  De  Romas  repeated 
his  experiments,  and  obtained  sparks  of  surprising  size.  "  Let 
the  reader  only  imagine,"  says  he,  "streaks  of  fire  from  9  to  10 
feet  in  length,  and  1  inch  in  breadth,  accompanied  by  a  cracking, 
which  was  louder,  or  as  loud,  as  a  pistol  shot.  In  less  than  an 
hour  I  obtained  at  least  thirty  such  sparks,  not  to  count  the  thou- 
sands which  were  7  feet  long,  or  less." 

Notwithstanding  the  measures  of  precaution  taken  by  this 
skilful  experimentalizer,  he  was  struck  down  by  the  violence  of 
the  charge. 

These  experiments  prove  most  completely  that  lightning  is  only 
an  electric  spark. 

Electricity  during  a  Thunder-storm.— On  examining  the  elec- 
trical condition  of  the  clouds  which  gradually  pass  over  the  kite, 
we  perceive  that  they  are  sometimes  charged  with  positive  or  ne- 
gative electricity,  and  sometimes  in  a  natural  condition.  Although 
we  know  nothing  of  the  distribution  of  electricity  in  the  clouds, 
the  attraction  and  repulsion  of  the  unequally,  or  equally  electrified 
clouds,  is  doubtlessly  the  cause  of  the  extraordinary  motions  ob- 

52* 


618  ELECTRICITY    DURING   A    THUNDER-STORM. 

served  in  the  heavens  during  a  thunder-storm.  During  this  gene- 
ral agitation  of  the  atmosphere,  we  see  lightning  flash  through  the 
sky,  and  hear  the  thunder  roll.  These  phenomena  we  are  now 
about  to  consider  more  attentively. 

We  often  see  lightning  break  from  the  clouds,  and  flash  far 
across  the  sky.  On  observing  this  phenomenon  below  our  feet, 
from  high  mountains,  we  are  able  to  form  a  more  correct  idea  of 
its  extent,  and  all  observers  agree  in  stating  that,  under  similar 
circumstances,  they  have  observed  flashes  of  lightning  of  at  least  a 
German  mile  in  length  ;  we  also  know  that  several  flashes  proceed 
from  the  same  cloud ;  finally,  it  is  known  that  lightning  generally 
describes  a  zigzag  line ;  this  form  is  common  to  lightning,  and  to 
the  electric  spark. 

The  vesicles  of  vapor  which  form  clouds  are  not  such  perfect 
conductors  as  metals  ;  and  although  we  do  not  know  the  laws  of 
equilibrium,  and  the  distribution  of  electricity  in  imperfect  con- 
ductors, it  is  still  evident  that  they  do  not  perfectly  discharge 
themselves  at  once,  and  that  they  can  be  brought  back  to  their 
natural  condition  by  a  few  sparks;  this  explains  the  reason  why 
the  same  cloud  emits  several  flashes. 

The  length  of  the  lightning  appears  also  to  be  a  consequence 
of  the  imperfect  power  of  conduction  in  clouds,  and  the  mobility 
of  the  particles  of  which  they  consist.  We  may  obtain  sparks  of 
1  metre  in  length,  through  dry  air,  from  the  conductor  of  the  best 
kind  of  electrical  machines ;  the  sparks,  however,  are  still  longer 
when  carried  off  over  woollen  or  silk  substances  that  have  been 
scattered  over  with  dust ;  in  the  same  manner  we  should  also 
obtain  longer  sparks  through  a  mist,  if  it  did  not  too  much  dimin- 
ish the  tension  of  the  electricity.  In  order  to  explain  the  length 
of  the  lightning  we  must  assume  that,  on  the  course  which  it  takes, 
the  particles  of  vapor  are  already  electrified  by  induction,  and  that 
finally,  when  the  lightning  appears,  the  disturbed  equilibrium  is 
restored  from  one  layer  to  another,  and  that,  to  a  certain  extent, 
sparks  only  pass  from  one  particle  to  another,  while  the  electric 
fluid  does  not  traverse  the  whole  course  intervening  between  the 
remotely  separated  clouds. 

Thunder  is  not  more  difficult  to  explain  than  the  noise  of  a 
small  electrical  spark,  and  arises  from  the  vibrations  of  the 
powerfully  agitated  air.  We  see  the  light  along  the  whole  course 
of  the  lightning,  and  the  report  arises  simultaneously  upon  the 


EFFECTS    OF    LIGHTNING    UPON    THE    EARTH.  619 

whole  extent  of  the  line;  as,  however,  sound  is  more  slowly 
propagated  than  light,  traversing  only  1125  feet  in  one  second, 
we  see  the  lightning  before  we  hear  the  thunder;  an  observer, 
standing  near  one  end  of  the  course  of  the  lightning,  will  not  at 
once  hear  the  sound  arising  simultaneously  at  all  points.  If  we 
assume  that  the  lightning  is  4500  yards  distant,  and  the  observer 
stands  in  the  prolongation  of  its  course,  the  sound  will  reach  him 
from  the  most  remote  extremity  of  the  lightning,  only  12  seconds 
later  than  from  the  part  lying  nearest  to  him.  As,  consequently, 
sound  reaches  the  ear  of  the  observer  only  by  degrees  from  dif- 
ferent parts  of  the  flash,  he  does  not  hear  an  instantaneous  noise, 
but  a  more  or  less  prolonged  rolling  of  the  thunder,  increased  in 
intensity  by  the  echo  of  the  clouds,  and  the  duration  of  this 
sound  depends  upon  the  length  of  the  lightning,  and  the  position 
of  the  observer  with  regard  to  its  course. 

Not  only  during  thunder-storms,  but  even  during  a  clear  state 
of  the  atmosphere,  we  may,  by  aid  of  a  good  electroscope,  show 
the  existence  of  an  electrical  tension  in  the  atmosphere. 

With  regard  to  the  origin  of  atmospheric  electricity,  we  actually 
know  nothing,  although  a  very  great  deal  has  been  written  on 
this  subject.  Some  are  of  opinion  that  the  electricity  of  thunder- 
clouds originates  in  a  rapid  condensation  of  the  atmospheric 
aqueous  vapor,  and,  therefore,  that  electricity  is  a  consequence 
of  the  rapid  formation  of  dense  clouds. 

Effects  of  Lightning  upon  the  Earth. — If  we  suppose  that  a 
thunder-cloud  hovers  from  2  to  6  thousand  yards  above  the  sea, 
or  over  a  large  lake,  and  if  we  assume  it  to  be  charged  with 
positive  electricity,  it  will  act  inductively,  the  -f  electricity  in 
the  water  will  be  repelled,  and  the  —  accumulated  upon  the 
surface  of  the  water ;  this  accumulation  may  be  sufficiently  great 
to  occasion  a  marked  elevation  of  the  water,  being  able  to  form 
a  large  wave,  a  water  mountain,  as  it  were,  which  will  continue 
as  long  as  the  electrical  condition  lasts;  this  latter,  however,  may 
terminate  in  three  different  ways. 

1.  When  the  electricity  of  the  cloud  is  gradually  dissipated 
without  any  discharge  taking  place,  the  naturally  electrical  con- 
dition of  the  water  will  thus  by  degrees  be  restored.  2.  When  a 
flash  passes  between  the  thunder-clouds,  or  a  flash  takes  place 
between  the  cloud  and  some  remote  places  on  the  earth,  conse- 
quently, when  the  cloud  is  suddenly  discharged,  the  electricity 


620  EFFECTS    OF    LIGHTNING    UPON    THE    EARTH. 

accumulated  on  the  surface  of  the  mountain  of  water,  quickly 
flows  off,  and  is  replaced  by  its  opposite  kind,  and  equilibrium  is 
in  this  manner  at  once  restored.  3.  When  the  thunder-cloud  is 
near  enough,  and  sufficiently  strongly  charged  with  electricity, 
the  lightning  passes  over.  This  direct  stroke  generally  occasions 
a  more  considerable  swelling  up  of  the  water  than  the  back- 
stroke. Such  a  shock  cannot  take  place  without  producing  a 
mechanical  action  upon  the  ponderable  elements. 

We  will  now  consider  the  actions  of  thunder- clouds  upon 
land. 

A  gradual  separation  and  reunion  of  the  electricity  produces 
no  visible  actions;  it  appears,  however,  that  such  disturbances 
of  the  electrical  equilibrium  may  be  felt  by  organic  beings, 
and  have  been  experienced  by  persons  affected  with  nervous 
diseases. 

The  back-stroke  is  always  less  violent  than  the  direct  shock; 
and  there  is  no  evidence  extant  of  its  having  occasioned  ignition, 
although  there  is  no  lack  of  examples  showing  that  men  and 
animals  have  been  struck  dead  by  it ;  in  these  cases  the  bodies 
have  no  limbs  broken,  and  present  no  trace  of  wounds  or  marks 
of  burns. 

The  direct  stroke  produces  the  most  fearful  actions;  on  the 
lightning  striking,  it  marks  the  spot  where  it  struck  the  ground 
by  one  or  more  holes  of  various  depths. 

Everything  that  is  raised  above  the  surface  is,  therefore,  pecu- 
liarly exposed  to  the  stroke  of  the  lightning ;  hence,  it  happens 
that  animals  are  struck  down  in  the  middle  of  a  plain :  other  cir- 
cumstances being  the  same,  one  is,  however,  safer  upon  a  non- 
conducting than  on  a  good  conducting  surface. 

Trees  are  good  conductors,  owing  to  the  sap  circulating  in 
them ;  when  a  thunder-cloud  passes  over,  a  strong  accumulation 
of  electricity  takes  place  in  the  trees,  and  on  this  account  we  say 
with  justice  that  trees  attract  the  lightning:  we  ought  never, 
therefore,  to  seek  protection  during  a  thunder-storm  under  trees, 
especially  under  such  as  stand  alone,  or  even  under  bushes  stand- 
ing exposed  on  a  plain.  Buildings  are,  generally  speaking, 
constructed  of  metal,  stone,  and  wood.  The  action  of  thunder- 
clouds on  these  substances  varies  with  the  difference  of  their 
nature.  When  the  lightning  strikes,  it  especially  attacks  the 
better  conductors,  whether  they  are  free  or  surrounded  by  worse 


MECHANICAL    ACTIONS    OF    LIGHTNING.  621 

conductors;  the  distributing  force  of  the  atmospheric  electricity 
acts  as  well  upon  the  nail  driven  into  the  wall,  as  upon  the 
weather-cock  projecting  in  the  air. 

The  mechanical  actions  of  lightning  are  usually  very  violent. 
When  lightning  strikes  a  room,  the  furniture  is  thrown  down  and 
broken,  and  metallic  substances  are  torn  out  and  hurled  far 
away.  Trees  are  cleft  and  split  asunder  by  lightning ;  we  are 
usually  able  to  trace  a  deep  furrow,  many  centimetres  in  breadth, 
which  runs  from  top  to  bottom,  the  peeled  bark  and  the  torn 
splinters  may  be  found  thrown  far  off,  and  we  often  observe  at 
the  bottom  of  the  tree  an  aperture  through  which  the  electrical 
fluid  passed  into  the  ground. 

The  physical  actions  of  lightning  show  a  more  or  less  conside- 
rable elevation  of  temperature.  When  lightning  strikes  a  straw 
shed,  dry  wood,  or  green  trees,  a  carbonization,  or  even  ignition 
takes  place ;  in  trees  there  is  seldom  any  trace  of  the  former. 
Metals  are  strongly  heated,  melted,  or  volatilized  by  the  lightning. 
Repeated  strokes  on  high  mountains  produce  evident  traces  of 
fusion. 

Lightning-conductors  consist  of  a  pointed  metallic  rod,  project- 
ing into  the  air,  and  of  a  good  conductor  connecting  the  rod  with 
the  ground.  The  following  conditions  must  be  fulfilled  where 
these  instruments  effect  the  purposes  for  which  they  are  designed: 

1.  The  rod  must  terminate  in  a  very  fine  point. 

2..  The  connection  with  the  ground  must  be  perfect. 

3.  No  interruption  must  occur  from  the  point  to  the  lower  part 
of  the  conducting  rod. 

4.  All  parts  of  the  apparatus  must  have  the  same  dimensions. 
When  a  thunder  cloud  hovers  over  the  lightning-conductor, 

the  combined  electricities  of  the  rod  and  the  conducting  medium 
will  be  decomposed,  the  electricity  will  be  repelled,  which  is  the 
same  as  the  one  contained  in  the  cloud,  and  diffuse  itself  freely 
in  the  earth,  whilst  the  opposite  electricity  will  be  attracted  to- 
wards the  point,  whence  it  can  flow  freely  into  the  air,  and  thus 
an  accumulation  of  electricity  in  the  lightning-conductor  will  be 
rendered  impossible.  Whilst  the  conductor  is  thus  inactivity, 
and  the  opposite  electricities  pass  through  it  in  an  opposite  direc- 
tion, we  may,  without  danger,  approach  and  even  touch  it,  since 
no  discharge  is  to  be  feared  when  there  is  no  electrical  tension. 
If  we  assume  that  one  of  the  three  first  named  conditions  is 


622 


LIGHTNING-CONDUCTORS. 


Fig.  533.  Fig.  534.      Fig.  535. 


not  fulfilled,  that  the  point  is  blunt,  the  medium  conducting  into 
the  ground  imperfect  or  interrupted,  it  is  evident  that  an  accumu- 
lation of  electricity  in  the  lightning-conductor  will  not  only  be 
possible,  but  even  unavoidable  ;  it  will  then  form  a  charged  con- 
ductor, in  which  an  immense  mass  of  electricity  will  be  accumu- 
lated, from  whence  we  may  draw  stronger  or  weaker  sparks. 

If  only  the  point  be  blunt,  the  lightning  may  strike,  but  it  will 
follow  the  conducting  medium  without  destroying  the  building. 

If  the  conducting  medium  be  interrupted,  or  the  connection 
with  the  ground  imperfect,  the  lightning  may  likewise  strike  ;  it 
will,  however,  distribute  itself  laterally  to  other  conductors,  and 
occasion  the  same  disturbances  that  would  occur  if  there  were  no 
lightning-conductor. 

Yet  more  :  a  lightning-conductor  having  this  deficiency  is  very 
dangerous  even  where  the  lightning  does  not  strike ;  for  when  at 

any  part  of  the  conducting  medium, 
the  electricity  is  sufficiently  accumu- 
lated, a  spark  may  strike  sideways,  and 
crush  or  set  fire  to  any  objects.  We 
may  illustrate  this  by  the  following 
melancholy  incident.  Richmann,  Pro- 
fessor of  Physics  at  St.  Petersburg, 
was  suddenly  struck  dead  by  the  emis- 
sion of  a  spark,  which  escaped  from 
the  lightning  conductor  attached  to  his 
house,  the  connecting  medium  of  which 
he  had  interrupted,  in  order  to  examine 
the  electricity  of  the  clouds.  Sokolow, 
engraver  to  the  Academy,  saw  the 
spark  strike  Richmann  on  the  forehead. 
After  having  stated  what  conditions 
must  be  fulfilled,  in  order  to  make  a 
lightning-conductor  efficient,  and  what 
dangers  may  ensue  from  the  neglect  of 
these  precautions,  there  still  remains 
something  to  be  said  of  the  practical 
arrangement  of  this  apparatus.  Gay- 
Lussac,  under  the  auspices  of  the 
Academy  of  Sciences,  has,  at  the  sug- 
gestion of  the  Minister  of  the  Interior,  drawn  up  instructions  rela- 


LIGHTNING-CONDUCTORS. 


623 


live  to  this  subject,  which  leave  nothing  more  to  be  desired,  but 
from  which  we  can  only  extract  the  most  essential. 

The  rod  of  the  lightning-conductor  is  about  9  yards  in  length ; 
it  is  composed  of  three  pieces,  namely,  an  iron  rod  of  8^  yards  in 
length,  a  brass  rod  of  18  inches,  and  a  platinum  needle  of  2 
inches  long;  taken  together  they  form  a  cone  sloping  upward  in  a 
regular  line.  See  Fig.  533. 

The  platinum  needle  is  soldered  to  the  brass  rod  with  silver, 
and  the  place  of  junction  surrounded  by  a  covering  of  copper,  as 
may  be  more  clearly  seen  in  Fig.  534. 

The  brass  rod  is  screwed  into  the  iron  rod,  and  thence  secured 
by  means  of  transverse  pins. 

The  iron  rod  is  often  composed  of  two  pieces  in  order  to  facili- 
tate its  transport ;  one  of  these  fastens  into  the  other  by  means  of 
a  long  conical  projection,  7  inches  in  length,  which  is  then  secured 
by  a  transverse  pin. 

In  Fig.  538  we  see  three  different  ways  in  which  the  rod  may 
be  fastened  to  buildings.  Under  the  rod,  about  3  inches  from 
the  roof  a  plate  V  b'  (see  Fig.  536)  is  screwed,  in  order  to  carry 
off  the  water  2  inches  above  this  plate,  the  rod  must  be  cylindri- 
cally  and  perfectly  well  turned,  in  order  that  a  large  screw  /  V 
Figs.  535  and  536  may  be  placed  round  it,  in  order  to  attach  the 
conducting  rod. 

The  conductor  is  a  quadrangular  iron  rod,  the  side  of  which 
measures  from  J  to  \  an  inch,  and  which  is  fastened  to  the  ring 
1 1  by  means  of  screws. 


Fig.  536.        Fig.  537. 


Fig.  538. 


624  LIGHTNING-CONDUCTORS. 

The  conducting  rod  is  carried  over  the  roof  and  down  the  build- 
ing into  the  ground.  Everything  depends  upon  bringing  the 
conducting  rod  in  as  good  a  connection  with  the  ground  as  pos- 
sible. If  there  happen  to  be  any  well  in  the  neighborhood,  which 
does  not  become  dry,  or  if  a  hole  can  be  bored  to  the  depth  at 
which  water  is  constantly  to  be  found,  it  is  sufficient  as  a  means 
of  conducting  the  rod,  if  we  divide  it  into  several  arms.  In  order 
to  increase  the  points  of  contact,  the  rod  is  conducted  through 
windings  to  the  well,  or  the  bore-hole,  which  must  then  be  filled 
with  charcoal. 

This  affords  the  double  advantage  of  protecting  the  iron  the 
better  from  rust,  and  placing  it  in  connection  with  so  good  a 
conductor  as  the  charcoal.  If  there  be  no  wrater  in  the  neighbor- 
hood, the  rod  must  at  least  be  connected  with  some  damp  spot  by 
means  of  a  long  canal  filled  with  charcoal.  To  effect  a  still 
greater  degree  of  security,  we  may  branch  the  conducting  rod  off 
into  several  lateral  canals. 

A  rope  twisted  round  with  copper  wire,  as  seen  in  Fig.  537,  is 
often  used  in  the  place  of  a  conducting  rod. 

As  we  may  easily  see  that  the  lightning  cannot  enter  a  con- 
ductor, constructed  according  to  these  principles,  it  will  also  as 
readily  be  understood  that  it  cannot  strike  within  some  distance 
of  the  lightning-conductor.  The  electricity  which  pours  copiously 
from  the  point,  will  be  attracted  by  the  thunder  cloud,  and  when 
it  has  reached  it,  it  neutralizes  a  part  of  the  original  electricity  of 
this  cloud. 

If,  therefore,  a  thunder  cloud  be  near  enough  to  the  lightning- 
conductor  to  act  inductively  on  it,  its  electrical  force  will  also 
be  weakened  by  the  efflux  of  the  opposite  electricity  from  the 
point.  The  nearer  the  cloud  approaches,  the  more  strongly  will 
its  inductive  force  act,  but  the  more  also  will  it  be  neutralized 
by  the  efflux  of  the  opposite  electricity. 

The  efficiency  of  the  lightning-conductor  depends,  however, 
likewise  on  other  conditions.  If  other  objects  near  it  project  be- 
yond it,  the  electricity  of  the  clouds  may  act  more  strongly  upon 
them  than  upon  it,  and  a  discharge  thus  take  place  ;  the  same  is 
the  case  when  there  are  any  considerable  masses  of  metal,  iron 
rods,  or  a  metallic  roofing  in  the  vicinity  of  the  lightning-con- 
ductor. In  the  latter  case,  we  must  bring  the  metallic  masses  into 


LIGHTNING-CONDUCTORS.  625 

as  good  a  connection  with  the  lightning-conductor  as  is  possible, 
in  order  that  the  attracted  electricity  may  flow  unhindered  through 
the  point.  It  is,  consequently,  dangerous  to  insulate  metallic  roofs 
from  the  conductors,  as  some  practical  philosophers  have  proposed 
doing.  Fortunately,  the  means  used  to  effect  such  an  insulation 
are  not  sufficient  for  the  purpose,  and  they  have  thus  produced 
only  useless  results. 

Experience  shows  us,  that  a  lightning-conductor  applied  with 
all  the  necessary  precaution,  and  of  the  dimensions  indicated,  is 
able  to  protect  a  circle  having  a  radius  of  about  20  yards. 


53 


INDEX. 


Aberration,  spherical,  264. 

Absolute  strength,  73. 

Absorption  of  gases,  by  liquids,  147. 

of  rays  of  heat,  543. 

Accelerated  and  retarded  motion,  150. 

Achromatic  prisms,  292. 

Achromatic  telescopes,  292. 

Achromatism  of  the  eyes,  304. 

Acid,  table  of  diluted  sulphuric,  107. 

, —  nitric,  107. 

,  433. 

Acoustics,  207. 

Action  of  the  windings  on  each  other, 
472. 

— —  of  an  electric  current  on  a  conduct- 
ing circuit  within  itself,  471. 

Adhesion,  77. 

between  solid  and  liquid  bodies,  108. 

Aggregate  conditions,  31. 

Air,  of  the,  116. 

,  decrease  of  temperature  in  the  up- 
per regions  of  the,  576. 

,  distribution  of  vapor  in  the,  589. 

is  dry,  the,  594. 

pressure  of,  119. 

is  damp,  594. 

purnp,  the,  132. 

,  combustible,  116. 

,  fixed,  116. 

waves,  formation  of  regular,  in  co- 
vered pipes,  227. 

,  electric  light  in  the,  and  in  other 

gases  under  the  pressure  of  the  atmo- 
sphere, 398. 

,  electric  light  in  rarefied,  399. 

bad  conductor  of  heat,  549. 

,  diurnal  and  annual  variation  in  the 

quantity  of  water  contained  in  the,  593. 

in  various  districts,  moisture  of  the, 

595. 

Alcoholmeter,  the,  102. 

of  Gay-Lussac,  104. 

Althans  of  Sayn,  191,  430. 

Amount  of  atmospheric  pressure,  table  of, 
124. 


Ampere's  experiments,  440. 

theory  of  magnetism,  467. 

Amplitude,  164. 

of  the  diurnal  variations,  361. 

Angle  of  deviation,  the,  69. 

of  reflection,  260. 

of  refraction,  270. 

Animal  electricity,  479,  482. 

heat,  551. 

Anode,  pole,  437. 

Archimedean  principle,  the,  90,  95. 

Areometer,  the,  96. 

of  Brissen,  and  G.  G.  Schmidt,  101. 

of  Beaume,  105. 

of  Cartier  and  Meisner,  105. 

of  Gay-Lussac,  101. 

,  the  graduated,  98. 

,  the  per  centage,  102. 

Armatures,  magnetic,  351. 

Atmospheric  electricity,  original  discovery 

of,  616. 

Atmosphere,  116. 
,  transmission  of  sound  through  the, 

217. 
',  electric  light  in  the  air,  and  in  other 

gases  under  the  pressure  of  the,  398. 
— — ,  of  the  pressure  of  the,  and  of  the 

winds,  578. 
Atmospheric  pressure,   measurement  of, 

120. 

amount  of,  124. 

moisture  of,  589. 


Atomic  weights,  the,  431. 
Atoms,  different  nature  of,  30. 
Attraction  between  solid  and  liquid  bodies, 

145. 

Atwood's  falling  machine,  152. 
August's  psychrometer,  593. 
Auditory  nerve,  251. 
Axes,  secondary,  281. 


B. 

Balance,  the,  67. 

,  sensibility  of  the,  70. 

,  hydrostatic,  95. 


628 


INDEX. 


Baldwin's  locomotive,  522. 
Ballr  Hero's,  141. 
Bars,  magnetization  of,  353. 
Barometer,  the,  121. 

,  height  of  the,  121. 

,  construction  of  the,  121. 

,  of  the  syphon,  122. 

,  measurement  of  heights  by  the,  130. 

,  Cavendish's  double,  400. 

,  causes  of  the  oscillations  in  the,  579. 

Barometric  gauge,  136. 

Battery,  Wollaston's  voltaic,  413. 

,  the  constant,  416. 

,  Grove's,  Bunsen's,  417,  419. 

,  Daniell's,  417. 

,  Smee's,  427. 

Beam  must  be  as  light  as  possible,  the,  70. 

Beaume's  areometer,  105. 

Becquerel's  constant-circuit,  416,  425. 

Bellies,  232. 

Bellows,  201. 

Bi-convex  glass  lens,  274. 

Blowers,  199. 

Body,  of  hard  and  soft.  73. 

,  of  brittle  and  ductile,  73. 

,  of  floating  and  submerged,  93. 

,  table  of  the  specific  weights  of  some 

solids,  105. 

Bohnenberger's  electroscope,  404. 
Brisson  and  G.  G.  Schmidt's  areometer, 

101. 

Bronchi,  246. 
Bunsen's  battery,  417. 


C. 


Calorimotor,  Hare's,  415. 

Calotype  paper,  345. 

Camera  obscura,  315,  344. 

Capillary  tubes,  108. 

Carlisle  and  Nicholson's  discovery,  421. 

Cartier's  scale,  105. 

Cathode,  pole,  437. 

Caustic  lines,  268. 

surface,  269. 

Cavendish's  double  barometer,  400. 
Celsius's  thermometer,  488. 
Central  motion,  158. 
Centripetal  forces,  159. 
Centrifugal  force,  162. 
Centre  of  gravity,  61. 

of  a  straight  line,  64. 

of  homogeneous  triangle,  64. 

of  triangular  pyramid,  64. 

of  a  cone,  65. 

of  a  regular  prism,  65. 

of  a  beam  must  lie  as  closely  as  pos- 
sible below  the  centre  of  suspension,  69. 
Chemical  actions  of  the  voltaic  piles,  421. 
Chladni,  216,  233. 
Chordae  vocales,  246. 
Circuit,  different  forms  of  the  galvanic,  412. 

,  theory  of  constant,  435. 

,  Becquerel's,  435. 

,  force  of  the  galvanic,  444. 

,  Becquerel's  constant,  416. 


Climate  on  land  and  at  sea,  572. 

Clock,  the  pendulum  of  a,  172. 

Clouds  and  mist,  596. 

Cloud,  cirrus,  598. 

,  cirro-cumulus,  cirro-stratus  and  nim- 
bus, 599. 

,  fleecy,  599. 

,  stratified,  599. 

-,  feathery,  accumulated,  599. 

Co-efficient  of  friction,  175. 

Colladon  and  Sturm,  experiments  of,  115. 

Color  of  the  spectrum  is  simple,  each,  287. 

,  complementary  of  the,  2S9. 

,  natural,  of  bodies,  289. 

of  contrast,  313. 

of  thin  plates,  335. 

of  the  sky,  606. 

Colored  rays  are  unequally  refrangible,  the 
differently,  286. 

rings,  (with  a  colored  plate,)  335. 

secondary  images,  312. 

shadows,  314. 

Combined  electricities,  390. 

Combustible  air,  116. 

Common  syphon,  127. 

Communicating  vessels,  89. 

Communication  of  electricity,  373. 

Compass,  the  tangent,  443. 

,  declination,  357. 

,  mariner's,  357. 

of  inclination,  358. 

Composition  of  forces,  43. 

Composite  eyes,  297. 

Compound  microscope,  320. 

Compressibility,  30. 

Concave  spherical  mirrors,  of,  262. 

mirrors,  images,  produced  by,  265. 

Condenser,  the,  396. 

Condensing  pump,  the,  139. 

Conducting  tubes,  influence  of  the,  183. 

Conductors  and  non-conductors,  369. 

Connection  between  the  particles  of  a  li- 
quid, 110. 

Constant  battery,  the,  416. 

Construction  of  the  voltaic  pile,  407. 

of  the  barometer,  121. 

Contact,  theory  of,  436. 

Contrast,  colors  of,  313. 

Convex  lenses,  simple  eyes  with,  298. 

mirrors,  268. 

Cornea,  298. 

Coulomb's  plan,  352. 

Cubic  expansion,  490. 

Current,  magnetic  actions  of  the,  454. 

,  magnetization  by  the  galvanic,  454. 

,  as  a  moving  force,  application  of  the 

galvanic,  456. 

,  induction  of  the,  470. 

,  by  the  influence  of  terrestrial  mag- 
netism, direction  of,  463. 

and  magnets,  fotation  of  movable, 

469. 

and  animal  electricity,  thermo-elec- 
tric, 479. 

Crystaline  lens,  298. 

Crystalization,  78. 

Crystalography,  79. 


INDEX. 


629 


Crystals,  78. 
Cylinder,  the  inclined, 


D. 


Daguerre's  discovery,  344. 
Daniel's  battery,  417. 

hygrometer,  591. 

Davy's  discovery,  344,  423. 
Dechalle's  experiments,  155. 
Declination  of  the  magnet,  354. 

compass,  357. 

,  variations  of,  360. 

Delezeune,  table  of  dilute  sulphuric  acid, 

107. 

Density,  39. 

De  Romas'  experiments,  617. 
Despretz's  experiments,  549. 
Dew  point,  592. 

,  the,  595. 

Differently  (the)  colored  rays  are  unequally 

refrangible,  286. 
Dilute  sulphuric  acid,  table  of,  107. 

nitric  acid,  table  of,  107. 

Diminution  of  magnetic  force  by  distance, 

364. 
of  electrical  power  with  the  increase 

of  distance,  387. 
Dioptrics,  270. 
Dipping  needle,  358. 
Direction  of  motion,  148. 
of  magnetic,  declination,  inclination, 

354. 

Disc,  a,  66. 
Dispersing  power  of  different  substances, 

291. 

Distance  of  distinct  vision,  301. 
Distinct  vision  at  different  distances,  299. 
Distribution  of  electricity  on  the  surfaces 

of  conducting  bodies,  387. 
Divisibility,  29. 
Db'bereiner's  lamp,  146. 
Dollond's  achromatic  telescopes,  292. 
Double  touch,  the,  354. 

refraction,  341. 

Dufay's  invention,  373. 

Duration  of  the  impression  of  light,  309. 


E. 


Earthquakes,  influence  on  the  magnetic 

needle,  361. 

Earth,  actions  of  lightning  upon  the,  619. 
Echo,  reflection  of  the,  224. 

multiple,  225. 

Efliux,  velocities  of  the,  ISO. 

of  liquids,  reaction  created  by  the, 

186. 

Elastic  fluids,  116. 
Elasticity,  72,  125. 

of  liquids,  115. 

Electric  light  in  the  air  and  in  other  gases 

under  the  pressure  of  the  atmosphere, 

398. 


Electric  light  in  rarefied  air,  399. 

fly-wheel,  401. 

•  currents,  capacity  of  metals  for  con- 
ducting, 452. 

currents  by  magnets,  induction   of, 

473. 

fluids  and  the  natural  condition  of 

bodies,  of  the,  371. 

pistol,  374. 

forces,  387. 

telegraph,  458. 

current  on  a  conducting  circuit  with- 
in itself,  action  of  an,  470. 

Electrical  actions,  368. 

•  diminution  of  power   with   the    in- 
crease of  distance,  387. 

Electricity,  of  the  two  kinds  of,  370. 

during  a  thunder-storm,  617. 

,  communication  of,  373. 

by  induction,  375. 

,  of  combined,  370. 

,  direct  proofs  of  the  development  of, 

by  contact,  403. 

,   distribution  of,  on  the  surfaces  of 

conducting  bodies,  387. 

,  original  discovery  of  atmospheric, 

616. 

Electrifying  machine,  the,  381. 

machine,  the  steam,  384. 

Electro-chemical  theory,  431. 

magnetic  telegraph,  459. 

Electrodes,  437. 

Electrolytic  law,  the,  433. 

Electrophorus,  the,  380. 

Electroscope  of  Bohnenberg,  404. 

Electrotype,  425. 

Elements,  resistance  of  the,  450. 

Emission,  or  corpuscular  theory,  326. 

Engine,  the  fire,  141. 

,  the  steam,  507. 

Equality  of  pressure,  principle  of  the,  76. 

Equilibrium,  65. 

offerees,  43. 

,  indifferent,  65. 

,  stable,  unstable,  65. 

,  molecular,  72. 

of  solids,  74. 

of  heavy  fluids,  83. 

of  floating   and  submerged   bodies, 

conditions  of  the,  93. 

— —  of  the  force  of  tension,  502. 

Escapement,  173. 

Evaporation,  530. 

,  production  of  cold  by,  534. 

Expansion,  485. 

of  solid  bodies,  the  co-efficient  of, 

499. 

of  fluids,  492. 

of  solid  bodies,  489. 

,  cubic,  490. 

of  gases,  493. 

Extensibility,  30. 

Eyes,  composite,  297. 

,  simple,  with  convex  lenses,  298 

,  achromatism  of  the,  304. 

,  vision  with  both,  307. 


53* 


630 


INDEX. 


F. 


Fahrenheit's  thermometer,  488. 

Falling  stars,  614. 

Faraday,  Mr.,  206,  437,  471. 

Fechner's  discovery,  438. 

Fire  engine,  the,  141. 

Fireballs,  614. 

Fixed  air,  116. 

Fleecy  clouds,  599. 

Floating  bodies,  93. 

Fluids  have  the  property  of  regularly  pro- 
pagating to  all  parts  the  pressure  exer- 
cised upon  a  portion  of  their  surface,  76. 

,  equilibrium  of  heavy,  83. 

,  pressure  of,  84. 

,  magnetic,  349. 

,  expansion  of,  492. 

Fly-wheel,  the  electric,  401. 

of  a  steam-engine,  511. 

Focal  lines,  268. 

distance,  279. 

Force,  centrifugal,  162. 

of  the  galvanic  circuit,  444. 

Forces,  composition  of,  43. 

,  parallelogram  of,  44. 

,  of  expansion  of,  118. 

,  centripetal,  159. 

Formation  of  regular  air-waves  in  covered 
pipes,  227. 

of  vapor,  498. 

Fourneyron,  experiences  of,  189. 

turbines,  190. 

Franklin's  plate,  391. 

Freezing  of  water  in  a  vacuum,  534. 

of  mercury,  535. 

Friction,  co-efficient  of,  175. 

,  sliding,  176. 

,  rolling,  177. 

,  resistance  of,  177. 

Fusion,  494. 


G. 

Gadiat,  simplifying  turbines  of,  190. 
Galileo,  inclined  plane  of,  116,  120,152, 

155. 

Galileo's  telescope,  322. 
Gay-Lussac's  areometer,  101. 

barometer,  122. 

Galvanometer,  441. 

Galvani's  discovery,  402. 

Galvanism,  402. 

Galvanic  circuit,  different  forms  of  the, 

412. 

current,   magnetic   actions  of  the, 

438. 

circuit,  force  of  the,  444. 

piles,  physiological   actions  of  the, 

419. 

Galvanic  currents,  generation  of  light  and 
heat  by,  420. 

,  magnetization  by  the, 


454. 


plication  of  the,  456. 


,  as  a  moving  force,  ap- 


I  Galvanic  currents,  on  each  other,  recipro- 
cal action  of,  465. 

Gases,  116. 

,  measurement  of  the  pressure  of,  143. 

,  absorption  of,  by  liquids,  147. 

,  motion  of,  197. 

,  the  laws  of  the  flow  of,  202. 

,  pressure  of  gases  in  the  flowing  out, 

205. 

,  expansion  of,  493. 

• for  conducting  heat,  capacity  of  li- 
quids and,  548. 
,  Gaseous  bodies,  116. 

Gasometer,  197. 

Graduated,  areometer  the,  98. 

Gravity,  34. 

,  centre  of,  61. 

of  liquids,  the  specific,  97. 

General  idea  of  physics,  25. 

Generation  of  light  and  heat  by  galvanic 
currents,  420. 

Grimaldi  and  Riccioli,  experiments  of,  155. 

Grotthuss'  discovery,  422. 

Grove's  battery,  419. 


H. 


Hail  and  snow,  603. 

Hail-storm,  604. 

Hair-hygrometer,  590. 

Halos  and  parhelia,  612. 

Hare's  calorimotor,  415. 

Heat,  by  galvanic  currents,  generation  of 
light,  420. 

,  of,  479. 

,  latent,'496. 

,  means  of  comparing  quantities  of, 

536. 

,  results  of  the  experiments  on  spe- 
cific, 538. 

,  existence  of  radiating,  539. 

,  absorption  of  rays  of,  543. 

,  capacity  of  bodies  to  radiate,  542. 

,  theoretical  views  concerning,  553. 

on  the  earth's  surface,  distribution 

of,  555. 

,  Ingenhousz's  apparatus  for,  548. 

,  reflection  and  diffusion  of  the  rays 

of,  544. 

,  capacity  of  bodies  to  transmit  ravs 

of,  545. 

by  conductors,  distribution  of,  547. 

,  capacity  of  liquids  and  gases  for  con- 
ducting, 548. 

by  chemical  combinations,  genera- 
tion of,  550. 

animal,  551. 

by  mechanical  means,  development 

of,  552. 

Hearing,  the  organ  of,  248. 
Height  of  the  barometer,  121. 
Hell's  achromatic  telescopes,  292. 
Henley's  discharging  rod,  395. 
Hero's  ball,  141. 

fountain,  142. 

Hoar-frost,  596. 
Homogeneous  triangle,  64. 


INDEX. 


631 


Homogeneous,  287 
Horizontal  water-wheels,  189. 
Humboldt's  description  of  the  rainy  sea- 
son, 602. 

Huyghen's  theory  of  undulation,  327. 
Hydraulic  press,  the,  81. 
Hydrostatics,  80. 

balance,  the,  95. 

Hygroscopic  bodies,  147. 
Hygrometers,  590. 
of  Daniel,  591. 


I. 


Ignis  fatuus,  613. 

Images  produced  by  concave  mirrors,  265. 

by  lenses,  282. 

,  colored  secondary,  312. 

Impediments  to  motion,  174. 

Inclined  plane,  the,  48. 

Inclination  of  magnets,  354. 

of  magnetic  needles,  357. 

,  variations  of,  360. 

Induction  currents,  470. 

of  electric  currents  by  magnets,  473. 

Inertia,  33. 

Influence  of  light  on  chemical  combina- 
tions and  on  decompositions,  343. 

Influence  of  conducting  tubes,  183. 

Ingenhousz's  apparatus  for  heat,  548. 

Insulated  pile,  the,  409. 

Intensity  of  tone,  223. 

of  light  diminishes  inversely  as  the 

square  of  the  distance,  256. 

of  terrestrial  magnetism,  361,  362. 

Interference  of  rays  of  light,  326. 

Iron  becomes  magnetic  under  the  influ- 
ence of  a  magnet,  349. 

,  influence  of  terrestrial  magnetism 

upori,  362. 

Isochimenal  lines,  570. 

Isothermal  lines,  567. 

,  causes  of  the  curvature  of  the, 

573. 

Jar,  the  Leyden,  393. 


K. 

Kobell's  discovery,  428. 
Kryophorus  of  Wollaston,  535. 


L. 

Lamp,  Db'bereiner's,  146. 
Lantern,  the  magic,  283. 
Larynx,  246. 
Latent  heat,  496. 

of  vapors,  530. 

Lateral  pressure  of  gases  in  the  flowing 

out,  205. 
Law  of  Mariotte,  128. 

of  Ohm,  447. 

Laws  of  the  oscillation  of  the  pendulum, 

164. 


Laws  of  the  change  of  winds,  586. 

of  the  flow  of  gases,  202. 

of  the  vibrations  of  blades  and  rods, 

242. 

,  the  electrolytic,  433. 

Lenses,  convex,  simple  eyes  with,  298. 

,  magnifying  the,  316. 

,  refraction  of  light  by,  274. 

Meniscus's,  275. 

Length  of  a  wave,  the,  202. 

Leslie's  differential  thermometer,  541. 

Lever,  the,  54. 

Leyden  jar,  the,  393. 

Light,  of,  252. 

,  intensity  of,  diminishes,  256. 

,  reflection  of,  258. 

,  refraction,  270. 

,  white,  298. 

recomposition  of,  287. 


,  electric,  in   the  air,  and   in   other 

gases  under  the  pressure  of  atmosphere, 
398. 

,  duration  of  the  impression  of,  309. 

,  interference  of  rays  of,  330. 

,  refrangibility  of,  331. 

,  white,  (with  a  colored  plate,)  334. 

,  polarization  of,  337. 

,  influence  of,  on  chemical  combina- 
tions and  on  composition,  343. 

in  rarefied  air,  electric,  399. 

and  heat  by  galvanic  currents,  gene- 
ration of,  420. 

Lightning  conductors,  389,  398,  621. 

plate,  a,  398. 

upon  the  earth,  actions  of,  619. 

Limits  of  visibility,  309. 

Linear-waves,  212. 

Lines,  isothermal,  567. 

,  isochimenal,  570. 

Liquids,  equilibrium,  80. 

specific  gravity  of,  97. 

elasticity  of,  115. 

compressibility  of,  115. 

absorption  of  gases  by,  147. 

in  motion,  lateral  pressure  of,  185. 

reaction  created,  by  the  efflux  of, 

186. 

,  and  gases  for  conducting  heat,  ca- 
pacity of,  548. 
Locomotive,  the,  520. 

Baldwin's,  522. 


Long-sightedness,  303. 
Luminous  point,  252. 


M. 

Machines   of  rotation,  magneto-electric, 
475. 

t  water-column,  192. 

,  the  electrifying,  381. 

,  the  steam-electrifying,  384. 

Magdeburg  hemispheres,  137. 
Magic  disc,  310. 

lantern,  the,  320. 

Magnet,  influence  of  a,  349. 
,  declination,  inclination,  354. 


632 


INDEX. 


Magnets  and  currents,  rotation  of  movable, 

469. 
,  induction  of  electric  currents   by, 

473. 
Magnetic  poles,  347. 

fluids,  349. 

actions  of  the  galvanic  current,  454. 

armatures,  351. 

north  pole  and  south  pole,  355. 

meridian,  the,  356. 

needles,  inclination  of  the,  357. 

equator,  359. 

force,  diminution  of,  by  distance,  364. 

Magnetism,  intensity  of  terrestrial,  361. 
Magnetization  of  steel  needles  and  bars, 

353. 

by  the  galvanic  current,  438. 

Magneto-electric,  470. 

machines  of  rotation,  475. 

Magnifying  lens,  the,  316. 

Manometers,  143,  201. 

Mariotte's  law,  128. 

Mass,  37. 

Material  pendulum,  170. 

Measures  and  weights,  36. 

Measurement    of  atmospheric    pressure, 

120. 
of  height  by  the  barometer,  of  the, 

130. 

of  the  pressure  of  gases,  of  the,  143. 

Mechanical  actions,  the,  621. 
Meiszner's  areometer,  105. 
Melloni's  thermomultiplicator,  541. 
Meniscus  lenses,  275. 
Mephitic  air,  116. 
Mercury,  of,  113. 

,  freezing  of,  535. 

Metals,  conductibility  of,  452. 
Meteoric  stones,  614. 
Meteorology,  555. 
Method,  26. 

of  mixtures,  the,  537. 

Microscope,  of  the  simple,  316. 

,  the  solar,  319. 

,  the  compound,  320. 

Middle-shot  wheel,  the,  189. 
Mirrors,  reflection  from  curved,  261. 

,  convex,  268. 

,  of  concave  spherical,  262. 

,  images  produced  by  concave,  265. 

Mist  and  clouds,  596. 
Moisture,  of  atmospheric,  598. 

,  degrees  of,  591. 

,  of  the  air  in  various  districts,  595. 

Molecular  forces,  32. 

equilibrium,  72. 

Monochord,  an  instrument,  241. 
Monsoons  and  trade-winds,  582. 
Motion  and  rest,  148. 

,  uniform,  the,  148. 

,  the  accelerated  and  retarded,  150. 

,  centra],  158. 

,  quantity  of,  168. 

,  impediments  to,  174. 

,  of  fluids,  179. 

,  of  gases,  197. 

,  of  vibratory,  207. 


Motion  occasioned  by  electrical  reaction, 
401. 

produced  by  the  discharge  of  elec- 
tricity, 400. 

Mount  d'Or,  124. 

Etna,  124. 

• Lebanon,  124. 

Movable  currents  and  magnets,  rotation 
of,  469. 

Miiller  (J.)  mosaic  composite  eyes,  297. 

Multiple  echoes,  225. 

Multiplicator,  the,  441. 

Miinchow,  289. 

Muschenbrock,  experiments  of,  74. 

Musical  notes,  236. 

Myopia,  303. 


N. 


Natural  colors  of  bodies,  289. 

Needles,  inclination   and   declination   of 

magnetic,  357. 

Nesselgrabe,  water-column  machines,  192. 
Newton's  industry,  161,  327. 
Nicholson's  areometer,  96. 
Nicholson  and  Carlisle's  discovery,  421. 
Niepce's  discovery,  344. 
Nitric  acid,  table  of,  107. 
Nobile's  multiplicator,  442. 


0. 


Oersted,  experiments  of,  115,  439. 

Ohm's  law,  447. 

Giber's  calculation,  300. 

Ombrometers,  600. 

Open  pipes,  the,  234. 

Optical  axes,  342. 

Optometers,  303. 

Organ-pipes,  233. 

Organs  of  speech,  the,  246. 

of  hearing,  the,  248. 

Origin  of  the  winds,  581. 
Oscillations,  164. 

in  the  barometer,  causes  of  the,  579. 

of  the  pendulum,  laws  of  the,  164. 

Otto  Von  Guericke's  invention,  132,  373. 


P. 


Papin's  digester,  528. 
Parallelogram  offerees,  44. 
Parhelia  and  halos,  612. 
Pendulum,  of  the,  163. 

,  laws  of  the  oscillations  of  the,  164. 

,  the  material,  170. 

of  a  clock,  the,  172. 

Phenakistiscope,  310. 

Photography,  344. 

Physical  actions  of  lightning,  621. 

Physiological  colors,  312. 

Physics,  what  is  understood  by,  26. 

Picard's  discovery,  400. 

Pile,  construction  of  the  voltaic,  407. 


INDEX. 


633 


Pile  of  Zamboni,  404. 

,  the  insulated,  409. 

,  the  closed,  410. 

,  the  dry,  410. 

properties  of  the  dry,  411. 

,  chemical  actions  of  the  voltaic,  421. 

,  thermo-electric,  481. 

Pipes,  organ,  233. 

,  open,  234. 

Pistol,  the  electric,  374. 
Plane,  inclined,  48. 

,  Galileo's  inclined,  151. 

of  incidence,  the,  270. 

Polarization  of  light,  337. 

Poles,  magnetic,  347. 

repel  each  other,  and  contrary  poles 

attract  each  other,  348. 
Poncelet's  wheel,  189. 
Porosity,  30. 
Porta's  invention,  315. 
Power  of  tension,  118. 
Presbyopia,  303. 
Pressure,  principle  of  the  equality  of,  76. 

of  fluids,  84. 

of  air,  119. 

,  measurement  of  atmospheric,  120. 

,  table  of  the  amount  of  atmospheric, 

124. 

of  gases,  measurement  of  the,  143. 

of  liquids  in  motion,  lateral,  185. 

of  gases  in  the  flowing  out,  205. 

of  the  atmosphere,  and  of  the  winds, 

578. 

Prism,  a,  272. 
Prisms,  refraction  of  light  in,  272. 

,  achromatic,  292. 

Projectiles,  158. 

Psychrometer,  593. 

Pulley,  the,  51. 

Pumps,  the  suction  of,  125. 

,  and  forcing  of  the, 

126. 

,  of  the  air,  132. 

,  condensing,  the,  139. 

Pupil,  289. 


Q- 

Quality  of  tone,  223. 
Quantity  of  motion,  168. 
of  rain,  600. 


Radiate  heat,  capacity  of  bodies  to,  542. 

Radiating  heat,  existence  of,  539. 

Rain,  quantity  of,  600. 

gauges,  600. 

between  the  tropics,  602. 

Rainbow,  the,  608. 

Rapidity  of  sounds,  224. 

Rays  of  heat,  reflection  and  diffusion  of 
the,  544. 

,  capacity  of  bodies  to  trans- 
mit, 545. 


Rays  of  heat,  absorption  of,  543. 

of  light,  interference  of,  326. 

Reaumur's  thermometer,  488. 
Reed-pipes,  242. 
Reflecting  telescope,  321. 
Reflection  of  light,  258. 

of  angles,  260. 

from  curved  mirrors,  261. 

Refracting  angle,  270. 

telescopes,  322. 

Refraction,  270. 

,  angle  of,  270. 

of  light  in  prisms,  272. 

by  lens,  274. 

,  double,  341. 

Refrangibility  of  light,  331. 
Regnault's  investigations  on  heat,  539. 
Reichenbach's  water-column,  192. 
Relation  between  the  perception   of  the 

eye  and  the  external  world,  305. 
Resistance  of  friction,  the,  77. 
Rest  and  motion,  148. 
Retarded   and   accelerated   motion,   the, 

150. 

uniformly,  150. 

Retina,  298. 

Riccioli  and  Grimaldi,  experiments  of,  155. 

Ring  colors,  (with  a  colored  plate,)  335. 

Rolling  friction,  177. 

Rumford's  differential  thermometer,  540. 


S. 


Safety  tubes,  the,  143. 

Salifiable  bases,  433. 

Salts,  decomposition  of,  423. 

Saussure's  hair-hygrometer,  590. 

Scale  of  tension,  405. 

Scheiner's  experiments,  302. 

Schweigger's  multiplicator,  441. 

Scoresby's  observations  on  snow,  603. 

Screw,  the,  50. 

Secondary  axes,  281. 

Secular  variations,  360. 

Segner's  water-wheel,  190. 

Sensibility  of  the  balance  increases  with 

the  length  of  the  beam,  the,  70. 
Shadows  and  half  shadows,  253. 

colored,  314. 

Short-sightedness,  303. 

Simple  eyes  with  convex  lenses,  298. 

microscopes,  316. 

Sky,  color  of  the,  606. 
Sliding  friction,  176. 
Snow  and  hail,  603. 
Solar  microscope,  the,  319. 
Solidification,  497. 
Sound  of  tone,  the,  223. 

,  velocity  of,  223. 

,  rapidity  of,  223. 

,  reflection  of,  224. 

Specific  gravity  of  liquids,  39. 

- of  some  solid  bodies,  ta- 


ble of,  97. 
Spectrum,  285. 
Speech,  organs  of,  246. 


634 


INDEX. 


Statics,  43. 

Steam,  the,  electrifying  machine,  384. 

engine,  the,  507. 

Steel  resists  the   magnetizing  influence, 
351. 

needles,  magnetization  of,  353. 

Stones,  meteoric,  614. 

Storms,  588. 

Strength,  67. 

Strings,  vibrations  of,  240. 

Sturm's  experiments,  115. 

Subjective  colors,  312. 

Suction,  the,  of  the  pumps,  126. 

and  forcing  of  pumps,  126. 

Sulphuric  acid,  table  of  dilute,  107. 
Suspension,  68. 
Syphon  barometer,  122. 

,  the,  121. 

,  common,  121. 


T. 


Table  of  the  specific  weight  of  some  solid 
bodies,  97. 

of  density  of  liquids,  106. 

of  the  amount  of  atmospheric  pres- 
sure, 120. 

Tangent  compass,  the,  443. 

Tangential  forces,  159. 

Telegraph,  the  electric,  458. 

Telescopes,  of  Hell's  Dollond's,  298. 

reflecting  and  refracting,  321. 

terrestrial,  325. 

Temperature  in  the  upper  regions  of  the 
air,  decrease  of,  576. 

,  diurnal  variations  of,  561. 

of  the  ground,  575. 

,  of  the  months,  and  of  the  year,  mean, 

562. 

of  forty-three  places,  mean,  565. 

Tension  of  the  vapor  of  water,  estimate  of 
the  force  of,  503. 

,  scale  of,  405. 

of  vapors,  maximum  of  the  force  of, 

500. 

Terrestrial  magnetism,  direction  of  cur- 
rents by  the  influence  of,  463. 

Thayer's  discovery,  428. 

Theory  of  constant  circuits,  435. 

—  of  contact  established  by  Volta,  436. 

Thermo-electric  currents,  and  animal 
electricity,  479. 

piles,  481. 

Thermo-multiplicator  of  Melloni,  541. 

Thermometer,  the,  485.- 

,  Reaumur's,  488. 

,  Fahrenheit's,  488 

,  Celsius',  488. 

,  differential,  Rumford's,  Leslie's, 

540,  541. 

,  observations  on  the,  559. 

Trough  apparatus,  the,  412. 

Thunder-storm,  electricity  during  a,  617. 

Time,  of  an  oscillation,  165. 

Talbot's  method,  345. 


Tones,  222. 

of  stretched  strings,  240. 

Torricellian  experiments,  121,  128,  129. 

,  vacuum  of  the,  121. 

,  theorem,  179. 

Trade-winds  and  monsoons,  582. 
Translucent  bodies,  253. 
Transmission  of  sound  through  the  atmo- 
sphere, 217. 

of  vibrations  of  sounds,  244. 

Transparent  bodies,  253. 

Turbines,  190. 

Tubes,  of  the  capillary,  108. 

safety,  the,  143. 

,  influence  of  conducting,  183. 

Tunica  sclerotica,  298. 
Tympanum,  cavity  of  the,  249. 


U. 

Udometers,  600. 
Undulatory  theory,  327. 
Uniform  motion,  the,  148. 
Uniformly  accelerated,  150. 
retarded,  150. 


V. 


Vapors,  latent  heat  of,  530. 

in  the  air,  distribution  of,  589. 

Vapor,  formation  of,  498. 

,  maximum  of  the  force  of  tension  of, 

500. 
of  water,  estimate  of  the  force  of 

tension  of  the,  503. 
Variations  of  declination  and  inclination, 

360. 

,  secular,  360. 

Velocity  of  efflux,  ISO. 
— —  of  sound,  223. 
Vertical  water-wheels,  187. 

,  under  shot,  187. 

,  over  shot,  189. 

,  middle  shot,  189. 


Vessels,  communicating,  89. 

Vibration,  theory  of,  326. 

Vibrations  of  different  strings,  240. 

.  of  sound  between  solid,  fluid,  and 
aeriform  bodies,  244. 

Vibratory  motion,  207. 

Vision  with  both  eyes,  307. 

Visibility,  limits  of,  309. 

Volta's  theory  of  contact,  436. 

experiments,  402. 

Voltaic  pile,  construction  of  the,  407. 

,  chemical  actions  of  the,  421. 

Voigtlander's  construction  of  the  camera 
obscura,  316. 

Volcanic  eruptions,  influence  on  the  mag- 
net, of  the,  361. 

Volkmann's  experiments,  305. 

Volumeter,  98. 


INDEX. 


635 


w. 

Water-column  machines,  192,  195. 

Water,  decomposition  of,  421. 

contained  in  the  air  diurnal  and  an- 
nual variation  in  the  quantity  of,  593. 

,  estimate  of  the  force  of  tension  of 

the  vapor  of,  503. 

in  a  vacuum,  freezing  of,  534. 

Water-spouts,  589. 

Water-waves,  209. 

Water-wheels,  189. 

horizontal,  189. 

— : of  Segner,  186. 

Wedge,  the,  51. 

Wedgwood's  discovery,  344. 

Weight,  36. 

of  some  solid  bodies,  table  of  speci- 
fic, 105. 


Weights  and  measures,  36. 

Windings  on  each  other,  action  of  the, 

Welter's  invention,  143. 
White  light,  285. 

recomposition  of,  287. 

Will-o'-the-Wisp,  613. 
Winds,  pressure  of  the,  578. 

,  origin  of  the,  581. 

in  higher  latitudes,  585. 

,  laws  of  the  change  of,  586. 

Wollaston's  battery,  413. 
•  kryophorus,  535. 


Z. 


Zamboni's  pile,  404. 


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and  divisions  mto  land  and  water,  mountain,  plain,  river,  and  lake  ;  its  meteorology   m  nera  'nrr! 
duction.,  vegetation,  and  animal  life;  estimating  and   analyzing  the  causes  at  wo'r  "and  I  '££ 
influence   on   plants,  ammals,  and   mankind.     A  study  such  as  this,  taken  in  conjunction 
ordinary  political  geography,  lends  to  the  latter  an  interest  foreign  to  the  mere  cataJogu    of  nam 
and  boundaries,  and,  in  addition  to  the  vast  amount  of  important  information  imparted    tendTto 
jmpress  the  whole  more  strongly  on  the  mind  of  the  student. 

Eulogy  is  unnecessary  with  regard  to  a  work  like  the  present,  which  has  passed  through  three 
editions  on  each  s,de  of  the  Atlantic  within  the  space  of  a  few  years.     The  publishers   therefore 
only  consider  it  necessary  to  state  that  the  last  London  edition  received  a  thorough  revision  at  the 
hands  of  the  author,  who  introduced  whatever  improvements  and  corrections  the  advance  of  sci 
ence  rendered  desirable  ;  and  that  the  present  issue,  in  addition  to  this,  has  had  a  careful  examina 
ion  on  the  part  of  the  editor,  to  ad.ipt  it  more  especially  to  this  co.antry.     Great  care  has  beei 
sxercised  m  both  the  text  and  the  glossary  to  obtain  the  accuracy  so  essential  to  a  work  of  this 
nature  ;  and  in  its  present  improved  and  enlarged  state,  with  no  corresponding  increase  of  price 
t  is  confidently  presented  as  in  every  way  worthy  a  continuation  of  the  striking  favor  with  whirh 
it  has  been  everywhere  received. 


From  William  Russell,  Esq.,  N.  E.  Normal  Institute 

Mass.,  March  14,  ]fc54. 

Mrs.  Spmerville's  volume  has  been  in  use  in  rar 
own  family  class  as  an  advanced  text-book  equalir 
acceptable  to  teacher  and  pupils.  But  the  new  edi- 
tion is  studied  with  peculiar  delight  from  its  happy 
blending  of  the  poetry  with  the  philosophy  of  the  sub- 
ject. I  know  of  no  class-book  more  instructive  or 

~~ —••«•*».      .rviujwis     0,1111     UUilCt'rS.         1    HOnC      U    Will    UC         m^t-**    iri1ur*>cf  itirr 

adopted  as  such  generally,  for  you  have  American-  m°re  " 

ized  it  and  improved  it  in  other  respects.  From  Thomas  Sherwin,  High  School,  Boston. 

From  Samuel  H  Taylor,  Esq  .  Philips  Academy,  I  hold  it  in  the  highest  estimation,  and  am  confident 

Andover.  Mass.,  Feb.  15,  lf-54.  that  it  will  prove  a  very  efficient  aid  in  the  education 

We  have  introduced  your  edition  of  Mrs.  Somer-  ot  the  young,  and  a  source  of  much  interest  and  in 

lies  "Physical  Geography"  into  our  school,  and  struction  to  the  adult  reader. 

Snd  it  an  admirable  work. 


From  Lieutenant  Maury,  U.  S.  N. 

National  Observatory,  Washington, 
thank  you  for  the  "Physical  Geography;"  it  is 
e,ap   ,  •    *  nave  keen  reading  it,  and  like  it  so  much 
I  have  made  it  a  school-book   lor  my  children, 
whom  I  am  teaching.    There  is,  in  my  opinion,  no 
work  upon  that  interesting  subjecton  which  it  treats- 
l  hysical  Geography— that  would  make  a  better  text 
book  in  our  schools  and  colleges.    I  hope  it  will  b> 


BLANCHARD    &    LEA'S    EDUCATIONAL    PUBLICATIONS. 


NOW  COMPLETE. 
A    SERIES    OF    TEXT-BOOKS!^  ON    PHYSICAL    SCIENCE. 

HANDBOOKS  OF  NATURAL  PHILOSOPHY  AND  ASTRONOMY, 

BY  DIONYSIUS  LARDNER,  D.  C.  L., 

Formerly  Professor  of  Natural  Philosophy  and  Astronomy  in  University  College,  London. 
This  valuable  series  is  now  complete,  consisting  of  three  Courses,  as  follows: — 

FIRST   COURSE, 

MECHANICS,  HYDROSTATICS,  HYDRAULICS,  PNEUMATICS,  SOUND,  AND  OPTICS, 

In  one  large  royal  12mo.  volume,  of  750  pages,  with  424  illustrations.     §1  75. 
SECOND    COURSE, 

HEAT,  MAGNETISM,  COMMON  ELECTRICITY,  AND  VOLTAIC  ELECTRICITY, 

In  one  royal  12mo.  volume,  of  450  pages,  with  244  illustrations.     $1  25. 
THIRD   COURSE, 

ASTRONOMY  AND    METEOROLOGY. 

In  one  very  large  royal  12mo.  volume,  of  nearly  800  pages,  with  37  plates  and  over  200 
illustrations.     $2  00. 

These  volumes  can  be  had  either  separately  or  in  uniform  sets,  containing 

About  two  thousand  pages,  and  nearly  one  thousand  Illustrations  on  Steel  and  Wood, 

To  accommodate  those  who  desire  separate  treatises  on  the  leading  departments  of  Natural 
Philosophy,  the  First  Course  may  also  be  had,  divided  in  three  portions,  viz : — 
Part  I.  MECHANICS.  Part  III.  OPTICS. 

Part  II.  HYDROSTATICS,  HYDRAULICS,  PNEUMATICS,  and  SOUND. 

It  will  thus  be  seen  that  this  work  furnishes  either  a  complete  course  of  instruction  on  these 
subjects,  or  separate  treatises  on  all  the  different  branches  of  Physical  Science. 

The  object  of  the  author  has  been  to  prepare  a  work  suited  equally  for  the  collegiate,  acade- 
mical, and  private  student,  who  may  desire  to  acquaint  himself  with  the  present  state  of  science, 
in  its  most  advanced  condition,  without  pursuing,  it  through  its  mathematical  consequences  and 
details.  Great  industry  has  been  manifested  throughout  the  work  to  elucidate  the  principles  ad- 
vanced by  their  practical  applications  to  the  wants  and  purposes  of  civilized  life,  a  task  to  which 
Dr.  Lardner's  immense  and  varied  knowledge,  and  his  singular  felicity  and  clearness  of  illustra- 
tion render  him  admirably  fitted.  This  peculiarity  of  the  work  recommends  it  especially  as  the 
text-book  for  a  practical  age  and  country  such  as  ours,  as  it  interests  the  student's  mind  by  show- 
ing him  the  utility  of  his  studies,  while  it  directs  his  attention  to  the  further  extension  of  that 
utility  by  the  fulness  of  its  examples.  Its  extensive  adoption  in  many  of  our  most  distinguished 
colleges  and  seminaries  is  sufficient  proof  of  the  skill  with  which  the  author's  intentions  have  been 
carried  out. 


From  Prof.  Kirkwood,  Delaware  College,  April  12, 1S51 . 
After  a  careful  examination,  I  am  prepared  to  say 
lhat  it  is  the  most  complete  "Handbook  of  Astrono- 
my" with  which  lam  acquainted.  I  trust  the  demand 
for  the  work  will  be  commensurate  with  its  merits. 

From  Prof.  A.  C  a  swell,  Broivn  University. 

April  29,  1854. 
I  regard  it  as  a  very  useful  and  very  convenient 

rpular  compend  of  the  sciences  of  which  it  treats, 
is  full  of  information  and  well  illustrated.    It  de- 
serves a  place  among  the  best  educational  treatises 
on  Astronomy  and  Physics. 

From  Prof.  W.  L.  Broivn,  Oakland  College,  Miss., 
March  29,  1854. 

I  consider  them  most  admirably  suited  for  ll»e  pur- 
poses designed  by  the  author— indeed,  as  the  very 
best  popular  works  on 'physical  science  with  which 
I  am  acquainted.  The  k<  Third  Course"  on  Astrono- 
my, is  especially  valuable  ;  its  magnificent  engrav- 
ings and  lucid  explanations  make  it  a  most  desira- 
ble text-book. 

From  Prof.  R.  Z.  Mason,  McKendree  College,  III. 

In  my  judgment  it  contains  the  best  selection  of 
compact  demonstrations  and  popular  illustrations  that 
we  have  yet  received  on  the  subject.  Dr.  Lardner 
has  relieved  it  somewhat  from  the  dry  details  of 
Mathematics,  and  yet  there  is  such  a  close  adherence 
to  severe  methods  of  thought  as  to  satisfy  the  most 
rigid  and  careful  analyst. 

From  Rev.  J.  G.  Ralston.  Norrittown,  Pa., 
March  22,  1854. 

Lardner's  Meteorology  and  Astronomy  is  a  fit  com- 


panion for  his  First  and  Second  Course.  It  is  won- 
derfully minute,  and  yet  not  prolix.  The  principles 
•of  Astronomy  are  probably  as  clearly  defined  and 
judiciously  arranged  in  this  book  as  they  can  be.  I 
expect  to  introduce  it  in  my  school. 

From  S.  Schooler,  Esq.,  Hnnover  Academy,  For., 
April  16,  Ib54. 

The  three  volumes  constitute  a  body  of  information 
and  detail  on  nearly  the  whole  range  of  physical 
science  which  is  not  to  be  found  together  in  any  other 
publication  with  which  I  am  acquainted.  I  hope 
that  these  works  may  be  the  means  of  inducing 
many  of  our  youth  to  devote  themselves  to  the  de- 
velopment of  the  Laws  of  Nature,  and  the  application 
of  them  to  industry,  and  that  they  may  be  the  vehicle 
for  conveying  sound  information  and  food  for  thought 
to  every  man  who  aspires  to  be  well  educated. 

From  M.  Conant,  State  Normal  School,  Mass  , 

April  11, 1854. 

This  is  a  treatise  admirably  adapted  to  its  purpose. 
For  the  accurate  knowledge  it  unfolds,  and  the  very 
popular  dress  it  appears  in,  I  think  I  have  met  with 
nothing  like  it.  I  shall  advise  the  students  of  the. 
Normal  School  to  add  this  to  your  edition  of  Lard- 
ner's Mechanics,  &c. 

From  Prof.  E.  Everett, -New  Orleans,  Feb.  25, 1854. 

I  am  already  acquainted  with  the  merits  of  this 
book,  having  had  occasion  to  consult  it  in  teaching 
the  branches  of  which  it  treats,  and  I  cannot  give  you 
a  stronger  assurance  of  my  high  opinion  of  it  than  the 
simple  fact  that  1  have  selected  it  as  the  text-book  of 
Physics  in  the  course  of  study  which  I  have  just  fixed 
upon  for  a  new  college  to  be  established  here. 


BLANGHARD   &  LEA'S    EDUCATIONAL    PUBLICATIONS. 


A  COMPLETE  COURSE  OP  NATURAL  SCIENCE-(Just  Issued.) 

THE    BOOK    OF    NATURE; 

AN  ELEMENTARY  INTRODUCTION  TO  THE  SCIENCES  OF 

Physics,  Astronomy,  Chemistry,  Mineralogy,  Geology,  Botany,  Zoology,  and  Physiology, 
BY  FREDERICK  SCHOEDLER,  Pn.  D.  * 

Professor  of  the  Natural  Sciences  af  Worms. 

FIRST  AMERICAN  EDITION, 
With,  a  Glossary,  and  other  Additions  and  Improvements. 

FROM  THE  SECOND  ENGLISH  EDITION,  TRANSLATED  FROM  THE  SIXTH  GERMAN  EDITION 

BY  HENRY  MEDLOCK,  F.  C.  S.,  &c. 

ILLUSTRATED  BY  SIX  HUNDRED  AND  SEVENTY-NINE  ENGRAVINGS  ON  WOOD. 

In  one  handsome  volume,  crown  octavo,  of  about  seven  hundred  large  pages,  extra  cloth.   $1  80. 

To  accommodate  those  who  desire  to  use  the  separate  portions  of  this  work,  the  publishers  have 
prepared  an  edition  in  parts,  as  follows,  which  may  be  had  singly,  by  mail  or  otherwise,  neatly 
done  up  in  flexible  cloth,  price  50  cents  each. 

NATURAL  PHILOSOPHY,  .... 

ASTRONOMY, 

CHEMISTRY, 

MINERALOGY  AND  GEOLOGY, 

BOTANY, 

ZOOLOGY  AND  PHYSIOLOGY, 

INTRODUCTION,  GLOSSARY,  INDEX,  Sec., 


114  pages,  with  149  Illustrations. 


64 
110 
104 


106 

96  pages. 


51 

48 
167 
176 

84 


The  necessity  of  some  acquaintance  with  the  Natural  Sciences  is  now  so  universally  admitted  in 
all  thorough  education,  while  the  circle  of  facts  and  principles  embraced  in  the  study  has  enlarged 
so  rapidly,  that  a  compendious  Manual  like  the  BOOK  OF  NATURE  cannot  fail  to  supply  a  want  fre- 
quently felt  and  expressed  by  a  large  and  growing  class. 

The  reputation  of  the  present  volume  in  England  and  Germany,  where  repeated  editions  have 
been  rapidly  called  for,  is  sufficient  proof  of  the  author's  success  in  condensing  and  popularizing 
the  principles  of  his  numerous  subjects.  The  publishers  therefore  would  merely  state  that,  in 
reproducing  the  work,  they  have  spared  no  pains  to  render  it  even  better  adapted  to  the  American 
student.  It  has  been  passed  through  the  press  under  the  care  of  a  competent  editor,  who  has  cor- 
rected such  errors  as  had  escaped  the  attention  of  the  English  translator,  and  has  made  whatever 
additions  appeared  necessary  to  bring  it  completely  on  a  level  with  the  existing  state  of  science. 
These  will  be  found  principally  in  the  sections  on  Botany  and  Geology;  especially  the  latter,  in 
which  references  have  been  made  to  the  numerous  and  systematic  Government  surveys  of  the 
several  States,  and  the  whole  adapted  to  the  nomenclature  and  systems  generally  used  in  this 
country.  A  copious  Glossary  has  been  appended,  and  numerous  additional  illustrations  have  been 
introduced  wherever  the  elucidation  of  the  text  appeared  to  render  them  desirable. 

It  is  therefore  confidently  presented  as  an  excellent  Manual  for  the  private  student,  or  as  a  com- 
plete and-thorough  Class-book  for  collegiate  and  academical  use. 

far  as  my  knowledge  extends.  It  admirably  com- 
bines perspicuity  with  brevity;  while  an  excellent 
judgment  and  a  rare  discrimination  are  manifest  in 
the  selection  and  arrangement  of  topics,  as  well  as  in 
the  description  of  objects,  the  illustration  of  pheno- 
mena, and  the  statement  of  principles.  A  more  care- 
ful perusal  of  those  departments  of  the  work  to  which 


Books  which  treat  of  everything  too  often  remind 
us  of  patent  medicines,  that  are  advertised  to  cure  all 
the  maladies  that  human  flesh  is  heir  to.  But  the 
volume  before  us  does  not  belong  to  that  genus.  It 
is  not  the  production  of  a  quack,  but  is  a  truly  scien- 
tific manual,  almost  a  library  on  Physical  Sciences, 
yet  perfectly  convenient,  and  valuable  to  the  student 
as  a  work  of  reference.  Though  the  whole  range  of 
sciences  is  embraced  in  it,  yet  it  affords  a  much  more 
minute  and  ample  fund  of  instruction  in  these  various 
departments  than  do  many  treatises  which  include 
only  a  single  subject.  Teachers  will  find  it  a  valu- 
able work  for  their  libraries.— N.  Y.  Student. 

Composed  by  the  same  distinguished  author,  all  the 
departments  have  a  uniformity  of  style  and  illustra- 
tion which  harmoniously  link  the  entire  circle  to- 
gether. The  utility  of  such  a  connected  view  of  the 
physical  sciences,  and  on  such  an  approved  basis,  is 
beyond  price;  and  places  their  acquisition  within 
the  reach  of  a  vastly  increased  number  of  inquirers. 
Not  only  to  such  is  it  valuable,  but  to  those  who  wish 
to  have  at  hand  the  means  of  refreshing  their  memo- 
ries and  enlarging  their  views  upon  their  favorite 
studies.  Of  such  a  book  we  gpeak  cordially,  and 
would  speak  more  at  length,  if  space  permitted.— 
Southern  Methodist  Quarterly  Revieiv. 

Froth  Prof.  Johnston.  Wesleyan  University,  Ct., 

March  14, 1854. 

I  dp  not  know  of  another  book  in  which  so  much 
that  is  important  on  these  subjects  can  be  found  in 
the  same  space. 

From  Prof.  Allen,  Oberlin  Institute,  Ohio,  April!,  1854. 

As  a  work  for  popular  instruction  in  the  Natural 

and  Physical  Sciences,  it  certainly  is  unrivalled,  so 


my  studies  have  been  particularly  directed  has  been 
abundantly  sufficient  to  satisfy  me  of  its  entire  reli- 
ableness—that the  object  of  the  author  was  not  so 
much  to  amuse  as  really  to  instruct. 

From  Prof.  Pearson,  Union  College,  N.  Y,  Feb.  22, 1?54. 

It  seems  to  be  a  book  well  adapted  to  imparting  ai: 
elementary  knowledge  of  Physics  and  Natural  His- 
tory to  students  of  our  Academies  and  Colleges. 
From  Prof.  /.  A.  Spencer,  N.  Y. 

I  am  delighted  with  Dr.  Schccdler's  "Book  of  Na- 
ture ;:)  its  tone  of  healthful  piety  and  reverence  for 
God's  word  add  a  charm  to  the  learning  and  deep  re- 
search which  the  volume  everywhere  manifests. 

From  W.  J.  Clark,  Esq.,  Georgetown  Female  Semi- 
nary, D.  C. 

As  far  as  I  have  examined,  it  has  afforded  me  great 
pleasure.     It  is  the  most  valuable  compendium  of  the 
subjects  of  which  it  treats  with  which  1  have  ever 
met. 
From  W.  H.  Allen,  President  ofGirard  College,  Philada. 

Though  a  very  comprehpusive  book,  it  contains 
about  as  much  of  the  details  of  natural  science  as 
general  students  in  this  country  have  time  to  study  in 
a  regular  academical  course;  and  I  am  so  well 
pleased  with  it  that  I  shall  recommend  its  use  as  a 
text-book  in  this  institution. 


BLANCHARD  &  LEA'S   EDUCATIONAL    PUBLICATIONS. 


TEXT-BOOK  OF  SCRIPTURE  GEOGRAPHY  AND  HISTORY— (Just  Issued.) 

OUTLINES  OF  SCRIPTURE  "GEOGRAPHY  AND  HISTORY; 

Illustrating  the  Historical  Portions  of  the  Old  and  New  Testaments, 

DESIGNED  FOR  THE  USE  OF  SCHOOLS  AND  PRIVATE  READING. 

BY  EDWARD  HUGHES,  F.R.A.S.,  F.G.S., 

Head  Master  of  the  Royal  Naval  Lower  School,  Greenwich,  &c. 

BASED  UPON  COLEMAN'S  HISTORICAL  GEOGRAPHY  OF  THE  BIBLE. 

"With,  twelve  handsome  colored  Maps. 

In  one  very  neat  royal   12mo.  volume,  extra  cloth.     $1  00. 

The  intimate  connection  of  Sacred  History  with  the  geography  and  physical  features  of  the  va- 
rious lands  occupied  by  the  Israelites,  renders  a  work  like  the  present  an  almost  necessary  com- 
panion to  all  who  desire  to  read  the  Scriptures  understandingly.  To  the  young  especially,  a  clear 
and  connected  narrative  of  the  events  recorded  in  the  Bible,  is  exceeding  desirable,  particularly 
when  illustrated,  as  in  the  present  volume,  with  succinct  but  copious  accounts  of  the  neighboring 
nations  and  of  the  topography  and  political  divisions  of  the  countries  mentioned,  coupled  with  the 
results  of  the  latest  investigations,  by  which  Messrs.  Layard,  Lynch,  Olin,  Durbin,  Wilson,  Stephens, 
and  others  have  succeeded  in  throwing  light  on  so  many  obscure  portions  of  the  Scriptures,  veri- 
fying its  accuracy  in  minute  particulars.  Few  more  interesting  class-books  could  therefore  be 
found  for  schools  where  the  Bible  forms  a  part  of  education,  and  none,  perhaps,  more  likely  to 
prove  of  permanent  benefit  to  the  scholar.  The  influence  which  the  physical  geography,  climate, 
and  productions  of  Palestine  had  upon  the  Jewish  people  will  be  found  fully  set  forth,  while  the  nu- 
merous maps  present  the  various  regions  connected  with  the  subject  at  their  most  prominent  periods. 

LIST   OF    MAPS. 

I.  The  World,  showing  the  Settlements  of  the  Descendants  of  Noah. 
II.  Canaan  in  the  time  of  the  Patriarchs. 

III.  Peninsula  of  Sinai,  with  part  of  Egypt;  illustrating  the  Journeyings  of  the  Israelites  from 

Egypt  to  Canaan. 

IV.  Canaa'n  as  divided  among  the  tribes  ;  illustrating  the  period  from  Joshua  to  the  Death  of  Saul. 
V.  Syria;   showing  the  Dominions  of  David  and  Solomon. 

VI.  The  Kingdoms  of  Judah  and  Israel. 

VII.  Assyria,  Chaldea,  and  Media.     Countries  of  the  Jewish  Captivities. 

VIII.  Palestine  under  the  dominion  of  the  Romans  in  the  time  of  our  Lord;  illustrating  the  Gos- 
pels and  Acts  of  the  Apostles. 
IX.  The  Countries  adjoining  the  Mediterranean;    illustrating  the  Acts  of  the  Apostles,  tha 

Epistles,  and  the  Apocalypse. 

X.  Mediaeval  Palestine  in  the  time  of  the  Crusades. 
XI.  Christendom  during  the  Crusades  ;  showing  the  extent  of  the  Roman  and  Greek  Churches, 

and  the  countries  professing  Mohammedanism. 
XII.  Modern  Palestine  under  Turkish  dominion. 


We  have  given  it  considerable  examination,  and 
have  been  very  favorably  impressed  with  it  as  a 
work  of  rare  excellence,  and  as  well  calculated  to 
answer  a  demand,  which,  so  far  as  our  knowledge 
extends,  has  never  yet  been  fully  accomplished. — 
Evangelical  Repository. 

A  concise  and  very  convenient  condensation  of 
just  such  facts  and  information  as  the  Biblical  student 
and  general  reader  want  always  at  hand.  We  com- 
mend it  without  reserve. — N.  Y.  Recorder. 

We  have  read  it  with  care,  and  can  recommend  it 
with  confidence.  Indeed,  we  do  not  know  of  a  more 
convenient  and  reliable  handbook  fora  pastor,  Sun- 
day-school teacher,  or  a  general  student  to  refer  to 
for  information  in  regard  to  Palestine,  whether  as  to 
its  physical  features  or  its  geography,  its  climate  or 
its  productions,  its  past  history  or  its  present  condi- 
tion.— Southern  Presbyterian. 

From  Prof.  Samuel  H.  Turher,  N.  Y.  Theological 
Seminary. 

It  appears  to  contain  in  a  compressed  form  a  vast 
deal  of  important  and  accurate  geographical  and 
historical  information  I  hope  the  book  will  have  the 
wide  circulation  which  iis  merits  entitle  it  to.  I  shall 
not  fail  to  recommend  it  so  far  as  opportunity  offers. 

From  Rev.  Samuel  Findley,  President  of  Antrim 

College,  Ohio,  Feb.  18, 1854. 

We  have  long  needed  just  such  a  book,  and  as  soon 
as  possible  we  shall  make  it  one  of  the  text- books  of 
oar  college.  It  should  be  a  text-book  in  all  our 
theological  institutions. 

From  Rev.  Eliphalet  Nott,  President  of  Union  College. 

N.  Y.,  Feb.  20,  1854. 

Few  more  interesting  class  books  where  the  Bible 
is  used  in  schools  can  be  found  than  the  "Outlines  of 
Scripture  Geography  and  History,"  and  it  will  prove, 


in  families  where  the  Bible  is  read,  a  valuable  aux- 
iliary to  the  understanding  of  that  blessed  volume.  It 
is  therefore  to  be  hoped  that  it  will  receive  that  patro- 
nage which  it  so  richly  deserves. 

From  Prof.  E.  Everett,  New  Orleans,  Feb.  25, 1854. 

I  have  studied  the  greater  portion  of  it  with  care, 
and  find  it  so  useful  as  a  book  of  reference  that  I  have 
placed  it  on  the  table  with  my  Bible  as  an  aid  to  my 
daily  Scripture  readings.  It  is  a  book  which  ought 
to  be  in  the  hands  of  every  biblical  student,  and  I  can- 
not but  hope  that  it  will  have  a  wide  circulation.  To 
such  as  desire  to  borrow  I  answer,  "  I  cannot  loan  it, 
for  I  am  obliged  to  refer  to  it  daily!" 

From  William  Russell,  N.  E.  Normal  Institute,  Mass., 

March  14, 1854. 

It  comprises  the  fullest  and  most  instructive,  as  well 
as  the  most  attractive  course  of  lessons  on  its  particu- 
lar subjects  that  has  hitherto  been  offered  in  the  com- 
pass of  a  single  volume. 

From  Prof.  Sturtevant,  Illinois  College,  March  25, 1854. 
Its  thoroughness  and  comprehensiveness  combined 
with  conciseness  and  portable  size,  and  especially 
its  neat  and  beautiful  maps,  render  it  peculiarly 
adapted  to  Bible  classes  and  Sabbath  schools,  and, 
indeed,  to  every  religious  family  and  every  reader  of 
the  Bible.  It  is  also  very  valuable  to  the  student  of 
Ancient  History,  whether  sacred  or  profane.  I  have 
seen  no  work  of  the  kind  which  pleases  me  so  well. 

From  Rev.  J.  G.  Ralston,  Norristown,  Pa., 

March  22,  1854. 

I  regard  it  as  an  excellent  book,  containing  more 
information  on  the  subjects  indicated  in  the  title  than 
any  other  with  which  I  am  acquainted.  It  cannot 
fail  to  be  a  popular  companion  with  every  student  of 
the  Holy  Scriptures.  I  take  pleasure  in  commending 
it  to  the  attention  of  my  pupils. 


^^1^L^!_^CATIONAL   PUBLICATIONS. 

NOW  COMPLETE" 

SCHMITZ  &  ZUMPT'S  CLASSICAL  SERIES 

The  publishers  have  much  nl^c,,™  :„  . 


teachers,  and  its  extensive  introduction  int  many  of  on  h  T  ^  "cholar'  and  P^tical 
the  objects  of  the  distinguished  editors  have  b^en  fuUv  c?rri/H  Sfminaries  and  co"eges,  show  that 
have  been  to  present  a  uniform  set  of  text-books  based  nth  '"  PreParation-  These  objects 
education,  conducting  the  student  from  the  commen  ^T  51™°?  aPProved  8ystems  of  modern 
one  definite  plan,  thus  relieving  the  teacher  froTthe  c  **  tO  their  concll^on  on 

works  based  upon  different  and  conflicting  systems  h^"^  °,  PaSSI"g  Progressively  through 
been  made,  which  are  printed  from  the  m^t  cor^  ^  Sele1Ct'°n  of  classical  authors  has 

with  biographical  and  critical  •SSJ^^^^^S^  texts'  and  are  Accompanied 


,as  ibeen  done  to 

convenient  for  use,  while  at  the  same  ^l^S       me  ™^lSmo'  form>  the?  "c 

low.     Every  care  has  been  taken  to  secure  the  verbaTandlh     7  ™  "e  unPrecede»tedly 

tional  works,  while  most  of  the  volume!  can  hlhad  in        ,      *  acc,urfcy  so  necess"7  in  educa- 
with  leather  backs  and  cloth  sides  "  neat  6Xtra  doth>  or  sironS^  half  bound, 

The  Series  consists  of  the  following  works-— 


ADVANCED   DAMMAR   OF   THE   LATIN  LANGUAGE.    Half  bound,  price 


the  RULES  °F  SYNTA 

'S  SHC?°°L    DJCTIONARY  OF   THE   LATIN   LANGUAGE.     In  two  parts, 
,  and  ENGLISH-LATIN.    Complete  in  one  very  thick  volume,  of  nearly  900  double- 
.olumned  pages,  full  bound  m  strong  leather.     Price  $1  30. 
Also,  PART  I,  LATIN-ENGLISH,  sold  'separate,  full  bound.     Price  90  cents. 
PART  II,  ENGLISH-LATIN,  sold  separate,  full  bound.    Price  75  cents. 

CORNELII  NEPOTIS  LIBER  DE  EXCELLENTIBUS   DUCIBUS  EXTERARUM  GENTIUM,  CUK 
\ms  CATONIS  ET  ATTICI.     With  Notes,  &c.     Price  in  extra  cloth,  50  cents  ;  half  bound,  55  JL 

C.  I  .  CJESARIS  COMMENTARII  DE  BELLO  GALLICO.     With  Notes,  Map,  and  other  illus- 
trations.    Price  in  extra  cloth,  50  cents;  half  bound,  55  cents. 

C.  C.  SALLUSTII  DE   BELLO   CATILINARIO  ET   JUGURTHINO.     With  Notes,  Map,  &c 
Price  in  extra  cloth,  50  cents;  half  bound,  55  cents. 

EXCERPTA  EX  P.  OVIDII  NASONIS  CARMINIBUS.    With  Notes,  &c.    Price  in  extra  cloth 
DO  cents  ;  half  bound,  65  cents. 

Q.  CURTII  RUFI  DE   GESTIS  ALEXANDRI  MAGNI  LIBRI  VIII.     With  Notes,  Map,  &c 
Price  in  extra  cloth,  70  cents;  half  bound,  75  cents. 

P.  VIRGILII  MARONIS  CARMINA  OMNIA.    Price  in  extra  cloth,  75  cents;  half  bound,  SO  cts. 

T.  LIVII  PATAVINI  HISTORIARUM,  LIBRI  I..  II.,  XXL,  XXII.     With  Notes,  two  colored 
Maps,  &c.     Price  in  extra  cloth,  70  cents  ;  half  bound,  75  cents. 

M.  T.  CICERONIS  ORATIONES  SELECTS  XII.    With  Notes,  &c.    Price  in  extra  cloth.  60 
cents  ;  half  bound,  65  cents. 

ECLOG.E  EX  Q,  HORATII  FLACCI  POEMATIBUS.     With  Notes,  &c.    Price  in  extra  cloth, 
60  cents;  half  bound,  65  cents. 

In  its  complete  state,  it  will    thus  be  seen  that  this  Series  presents  a  thorough  and   uniform 
course  of  instruction  in  Latin,  from  the  rudiments  to  the  lower  collegiate  classes. 

From  among  many  hundred  recommendatory  notices  with  which  they  have  been  favored,  the 
publishers  append  a  few. 


From  Prof.  N.  W.  Benedict,  Rochester  University,  N.  Y. 
I  have  taken  pains  to  examine  the  works  and  am 
rtappy  to  find  them  very  superior  for  Ihe  purposes 
designed.  The  selection  made  from  Latin  authors  is 
a  judicious  one;  the  editorial  labor  is  of  the  right 
kind;  and  the  mechanical  execution  of  the  works, 
together  with  the  low  price  at  which  they  are  afford- 
ed, constitute  them  a  valuable  aid  towards  the  fur- 
therance of  classical  studies  in  this  counlry. 


From  Prof.  W.  H.  Doherty,  Antioch  College,  Ohio. 

I  greatly  admire  the  beautiful  and  most  useful  se- 
ries of  Latin  authors  which  you  have  published.  I 
regard  them  as  a  real  boon  to  all  students  of  moderate 
means,  they  are  so  cheap,  so  comprehensive,  and  so 
correct.  They  constitute,  in  fact,  an  admirable  course 
of  Latin  reading,  and  their  wonderful  cheapness 
places  them  wi'hin  the  reach  of  the  humblest  and 
poorest  student. 


BLANCHARD  &  LEA'S  EDUCATIONAL   PUBLICATIONS. 


SCHMITZ  &  ZUMPT'S  CLASSICAL  SERIES— (Continued.) 


From  Prof.  J.  J.  Owen,  N.  Y.  Free  Academy. 
With  your  classical  series  I  am  well  acquainted, 
rnd  have  no  hesitancy  in  recommending  them  to  all 
my  friends  In  addition  to  your  Virgil,  which  we  use, 
we  shall  probably  adopt  other  books  of  the  series  as 
we  may  have  occasion  to  introduce  them. 

From  Reginald  PL  Chase,  Harvard  University,  Mass. 
I  have  taken  time  to  give  the  two  Grammars  a  par- 
ticularly careful  examination,  and  I  was  not  surprised 
to  find  them  equally  admirable  in  plan  and  execution 
with  the  other  works  of  your  series.  They  are  pre- 
cisely what  [  have  been  longing  for.  My  pupils  have 
provided  themselves  with  them,  and  they  will  here- 
after, in  common  with  the' other  volumes  of  the  series, 
lie  required  as  text-books  with  all  my  scholars.  In 
our  Latin  school  no  others  will  be  allowed. 

From  Prof.  A  Rollins,  Delaware  College. 
I  regard  this  series  of  Latin  text  books  as  decidedly 
superior  to  any  others  with  which  I  am  acquainted. 
TheLivy  and  Horace  I  shall  immediately  introduce 
for  the  use  of  the  college  classes. 

From  Prof.  A.  C.  Knox,  Hanover  College,  Ind. 
Having  examined  several  of  them  with  some  de- 
gree of  care,  we  have  no  hesitaiion  in  pronouncing 
them  among  the  very  best  extant. 

From  Prof.  R  N.  Newell.  Masonic  College,  Tenn., 
June  2,  1852. 

I  can  give  you  no  better  proof  of  the  value  which 
I  set  on  them  than  by  making  use  of  them  in  my  own 
classes,  and  recommending  their  use  in  the  prepara- 
tory department  of  our  institution.  I  have  read  them 
through  carefully  that  I  might  not  speak  of  them  with- 
out due  examination,  and  I  flatter  myself  that  my 
opinion  is  fully  borne  out  by  fact,  when  I  pronounce 


them  to  be  the  most  useful  and  the  most  correct,  as 
well  as  the  cheapest  editions  of  Latin  Classics  ever 
introduced  in  this  country.  The  Latin  and  English 
Dictionary  contains  as  much  as  the  sHvJenl  can  want 
in  the  earlier  years  of  his  course;  it  contains  more 
than  I  have  ever  seen  compressed  into  a  book  of  this 
kind.  It  ought  to  be  the  student's  constant  companion 
in  his  recitations.  It  has  the  extraordinary  recom- 
mendation of  being  at  once  portable  and  comprehen- 
sive. 

Among  the  various  editions  of  the  Latin  Classics. 
Schmitz  and  Zumpt's  series,  so  far  as  yet  published, 
are  at  all  times  preferred,  and  students  are  requested 
to  procure  no  other.—  Announcement  of  Bethany  Col- 
lege, Fa. 

But  we  cannot  forbear  commending  especially, 
both  to  instructors  and  pupils,  the  whole  of  the  series 
edited  by  those  accomplished  scholars.  Drs.  Schmitz 
and  Zumpt.  Here  will  be  found  a  set  of  text-books 
that  combine  the  excellences  so  long  desired  in  this 
class  of  works.  They  will  not  cost  the  student,  by 
one-half  at  least,  that  which  he  must  expend  for  some 
other  editions.  And  who  will  not  sny  that  this  is  a 
consideration  worthy  of  attention?  For  the  cheaper 
our  school-books  can  be  made,  the  more  widely  will 
they  be  circulated  and  used.  Here  you  will  find,  too. 
no  useless  display  of  notes  and  of  learning,  but  in 
foot-notes  on  each  page  you  have  everything  neces- 
sary to  the  understanding  of  the  text.  The  difficult 
points  are  sometimes  elucidated,  and  often  is  the  stu- 
dent referred  to  the  places  where  he  can  find  light, 
but  not  without  some  effort  of  his  own.  We  think 
that  the  punctuation  in  these  books  might  be  im- 
proved; but  taken  as  a  whole,  they  come  nearer  to 
the  wants  of  the  times  than  any  within  our  know- 
ledge.— Southern  College  Review. 


UNIFORM  WITH  SCHMITZ  &  ZUMPT'S  CLASSICAL  SERIES, 
BAIRD'S    CLASSICAL    MANUAL. 

THE  CLASSICAL  MANUAL;  AN  EPITOME  OP  ANCIENT  GEOGRAPHY,  GREEK  AND 
ROMAN  MYTHOLOGY,  ANTIQUITIES,  AND  CHRONOLOGY.  Chiefly  intended  for  the  use 
of  Schools.  By  the  Rev.  JAMES  S.  S.  BAIRD,  T.  C.D.,  Assistant  Classical  Master, 
King's  School,  Gloucester.  In  one  neat  royal  12nio.  volume.  Price  in  extra  cloth, 
50  cents;  half  bound,  55  cents. 

This  little  volume  has  been  prepared  to  meet  the  recognized  want  of  an  Epitome  which,  within 
the  compass  of  a  single  small  volume,  should  contain  the  information  requisite  to  elucidate  the 
Greek  and  Roman  authors  most  commonly  read  in  our  schools.  The  aim  of  the  author  has  been 
to  embody  in  it  such  details  as  are  important  or  necessary  for  the  junior  student,  in  a  form  and 
space  capable  of  rendering  them  easily  mastered  and  retained;  and  he  has  consequently  notincum- 
bered  it  with  a  mass  of  learning  which,  though  highly  valuable  to  the  advanced  student,  is  merely 
perplexing  to  the  beginner.  In  the  amount  of  information  presented,  and  the  manner  in  which 
it  is  conveyed,,  as  well  as  its  convenient  size  and  exceedingly  low  price,  it  is  therefore  admirably 
adapted  for  the  younger  classes  of  our  numerous  classical  schools. 

Although  issued  but  very  recently,  this  little  work  has  commanded  universal  approbation  ;  and 
its  immediate  introduction  into  a  large  number  of  our  best  educational  institutions,  sufficiently 
proves  that  the  author  has  succeeded  in  filling  a  vacancy  among  our  classical  text-books. 

From  Prof.  R.  W.  Newell,  Masonic  College,  Tenn. 
I  cannot  help  thinking  that  in  none  of  your  works 
have  you  so  effectually  provided  for  the  wants  of  the 
poor  student  as  in  this. 

From  Reginald  H.  Chase,  Harvard  University. 
That  invaluable  little  work,  the  Classical  Manual, 
has  been  used  by  me  for  some  time.  I  would  i,oton 
any  account  be  without  it.  You  have  i;ot  perhaps 
been  informed  that  it  has  recently  been  introduced  in 
the  High  School  of  this  place.  Its  typographical  ac- 
curacy is  remarkable. 


From  Prof.  J.  S.  Hart.  Principal  of  the  Philadelphia 

High  School.' 

!;Baird's  Classical  Manual"  is  an  admirable  com- 
pend  of  the  knowledge  most  indispensable  to  the  stu- 
iient  of  Greek  and  Roman  ajitiquities. 

From  Prof.  P.  13.  Spear,  Madison  University,  N.  Y. 

I  am  persuaded,  from  the  examination  whic'h  I  V  ave 
given  it.  that  if  a  class  were  to  be  drilled  upon  such 
an  '-Epitome"  as  this,  nothing  better  would  lay  a 
foundation  for  a  full  and  accurate  knowledge  of  the 
Geography,  Chronology,  Mythology,  and  Antiquities 
of  thtf  Grteks  and  Romans. 


ARNOT'S  ELEMENTS  OP  PHYSICS. 

ELEMENTS  OF  PHYSICS;  OR,  NATURALlffllO SOPHY,  GENERAL  AND  MEDICAL, 

Written  for  Universal  Use  in  Plain  or  Non-Technical  Language. 

BY  NEILL  ARNOT,  M.  D. 
In  one  octavo  volume,  leather,  with  about  two  hundred  illustrations.     $2  50. 


BLANCHARD  &  LEA'S  EDUCATIONAL  PUBLICATIONS 

BOLMAR'S  COMPLETE  FRENCH  SERIES. 


nranMOA  THEORE™AL  AND  PRACTICAL  GRAMMAR  OF 


of  a  correct  pronunciation  of  the  French.  In  oneP  18m..  vo^e,  half  bound 

E   TELEMAQOE.     In  on'e 


BOLMAR'S  SELECTION  OF  ONE  HUNDRED  OF  PERRIN"?  FARTT<V  *  •  j     •*». 

Key    containing  the  text  and  a  literal  and  a  free  translation,  arfatged  fn  SS&SS&S* 

tPion  o?tSe  F'ren  hrenTh  hTn  ^  ^Th  '"V^  English  Idi°m?  ^Iso,  a  figured  pronuncia- 
tion of  the  French.  The  whole  preceded  by  a  short  treatise  on  the  Sounds  of  the  French  I?n- 
guage  as  compared  with  those  of  English.  In  one  12mo.  volume,  half  bound  75  cents 
BOLMAR'S  BOOK  OF  FRENCH  VERBS,  wherein  the  Model  Verbs,  and  several  of  the  most 
difficult,  are  conjugated  Affirmatively,  Negatively,  Interrogatively,  and  Negatively  and  IrTte  - 
relatively,  containing  also  numerous  Notes  and  Directions  on  the  Different  Conjugations,  not  to 
be  found  m  any  other  book  published  for  the  use  of  English  scholars;  to  which  is  added  a  com- 
plete list  of  all  the  Irregular  Verbs.  In  one  12mo.  volume,  half  bound,  50  cents. 

The  long  and  extended  sale  with  which  these  works  have  been  favored,  and  the  constantly  in- 
creasing demand  which  exists  for  them,  renders  unnecessary  any  explanation  or  recommendation 
or  their  merits.  The  fact  that 

Over  two  hundred  thousand  volumes 

have  been  sold  is  the  best  evidence  that  their  long-continued  popularity  is  founded  on  their  intrinsic 
merit  and  skilful  adaptation  to  the  wants  of  the  student  and  teacher. 

BUTLER'S  ANCIENT  ATLAS. 

AN  ATLAS  OF  ANCIENT  GEOGRAPHY. 

BY  SAMUEL  BUTLER,  D.  D., 

Late  Lord  Bishop  of  LitchfieJd. 
In  one  handsome  octavo  volume,  half  bound,  containing  twenty-one  colored  Maps,  and  an 

Accentuated  Index.     $1  50. 

The  very  low  price  at  which  this  work  is  now  offered,  and  the  authoritative  position  which  it 
has  so  long  maintained,  render  it  a  very  desirable  reference  book  for  all  institutions  where  this 
branch  of  study  is  pursued.  Used  in  conjunction  with  the  following  volume,  it  forms  a  complete 
course  of  classical  geography. 


BUTLER'S  ANCIENT  GEOGRAPHY. 

GEOGEAPHIA   CLASSICA; 

OR,    THE    APPLICATION   OF   ANCIENT   GEOGRAPHY   TO   THE   CLASSICS. 

BY  SAMUEL  BUTLER,  D.  D., 

Late  Lord  Bishop  of  Litchfield. 
Sixth  American,  from  tlie  last  and  revised  London  Edition. 

WITH  QUESTIONS  ON  THE  MAPS,  BY  JOHN  FROST,  LL.  Dl,  &c. 
In  one  neat  volume,  royal  12mo.,  half  bound,  75  cents. 


MULLER'S    PHYSICS. 

PKINCIPLES  OF  PHYSICS  AND  METEOROLOGY. 

BY  PROF.  J.  MULLER. 

EDITED,  WITH  ADDITIONS,  BY  E.  E.  GRIFFITH,  M.  D. 

In  one  large  and  very  handsome  octavo  volume,  with  550  wood-cuts,  and  two  colored  plates.  $3  50. 
It  presents  a  systematic,  minute,  and  comprehen-  I  American  Editor,  of  articles  on  the  Electro  M 


sive  exposition,  in  one  middle-sized  volume,  of  all  the  I  Telegraph,  Electrotype,  Steam-engine,  &c.  The  en- 
most  important  facts  and  theories  relating  to  Statics,  j  graviiigs  in  this  volume  certainly  surpass  everything 
Hydrostatics,  Dynamics,  Hydrodynamics.  Pneuma-  I  of  the  kind  heretofore  published  in  America.  Taking 


tics,  the  Laws  of  the  Motions  of  Waves  in  general, 
Sound,  the  Theory  of  Musical  Notes,  the  Voice  and 


it  for  all  in  all,  we  know  of  no  single  work  which 
contains  ?o  satisfactory  treatises  on  so  great  a  num- 
ber of  subjects  connected  with  ihe  philosophy  of  na- 


Hearing,  Geometrical  and  Physical  Optics,  Heat  and 

Meteorology,  Magnetism,  Electricity  and  Galvanism,     lure.—  Mtthodist  Quarterly  Review. 

in  all  their  subdivisions  j  with  the  addition;  by  the 


BLANCHARD  &  LEA'S    EDUCATIONAL  PUBLICATIONS. 


SHAW'S  ENGLISH  LITERATURE— (Lately  Published.) 

OUTLINES  OF  ENGLISH  LITERATURE. 

'     BY  THOMAS  B.  SHAW, 

Professor  of  English  Literature  in  the  Imperial  Alexander  Lyceum,  St.  Petersburg. 

SECOND    AMERICAN   EDITION. 

WITH  A  SKETCH  OF  AMERICAN  LITERATURE. 

BY  HENRY  T.  TUCKERMAN,  Esa. 
In  one  large  and  handsome  volume,  royal  12mo.,  of  about  five  hundred  pages. 

Extra  cloth,  $1  15;  half  bound  in  leather,  $1  25. 

The  object  of  this  work  is  to  present  to  the  student,  within  a  moderate  compass,  a  clear  and 
connected  view  of  the  history  and  productions  of  English  Literature.  To  accomplish  this,  the 
author  has  followed  its  course  from  the  earliest  times  to  the  present  age,  seizing  upon  the  more 
prominent  "  Schools  of  Writing,"  tracing  their  causes  and  effects,  and  selecting  the  more  cele- 
brated authors  as  subjects  for  brief  biographical  and  critical  sketches,  analyzing  their  best  works. 
and  thus  presenting  to  the  student  a  definite  view  of  the  development  of  the  language  and  lite- 
rature, with  succinct  descriptions  of  those  books  and  men  of  which  no  educated  person  should 
be  ignorant.  He  has  thus  not  only  supplied  the  acknowledged  want  of  a  manual  on  this  subject, 
but  by  the  liveliness  and  power  of  his  style,  the  thorough  knowledge  he  displays  of  his  topic, 
and  the  variety  of  his  subjects,  he  has  succeeded  in  producing  a  most  agreeable  reading-book, 
which  will  captivate  the  mind  of  the  scholar,  and  relieve  the  monotony  of  drier  studies. 


From  Prof.  J.  V.  Raymond,  University  of  Rochester. 
Its  merits  I  had  not  now  for  the  first  time  to  learn. 
I  have  used  it  for  two  years  as  a  text-book,  with  the 
greatest  satisfaction.  It  was  a  happy  conception,  ad- 
mirably executed.  It  is  all  that  a  text  book  on  such 
a  subject  can  or  need  be.  comprising  a  judicious  se- 
lection of  materials,  easily  yet  effectively  wrought. 
The  author  attempts  just  as  much  as  he  ought  to,  and 
does  well  all  that  he  attempts;  and  the  best  of  the 
book  is  ihe  genial  spirit,  the  genuine  love  of  genius 
audits  works  which  thoroughly  pervades  it  and  makes 
it  just  what  you  want  to  put  in  a  pupil's  hands. 

Fran  Prof.  J.  C.  Pickard,  Illinois  College. 
Of  ';  Shaw's  English  Literature"  I  can  hardly  say 
too  much  in  praise.    I  hope  its  adoption  and  use  as  a 
text-book  will  correspond  to  its  great  merits. 

From  Edwin  Arnold,  Esq.,  Bel- Air,  Md. 
A  mo?t  valuable  contribution  to  our  slock  of  school- 
books.  It  supplies  a  vacuum  which  has  been  severe- 
ly felt  by  those  who  desired  to  communicate  to  their 
pupils  the  most  slender  ouilnie  of  belles-lettres.  In 
my  opinion,  it  is  itself  a  most  desirable  work,  and 
should  be  placed  in  the  hands  of  every  youth  as  soon 
as  old  enough  to  lay  aside  the  tales  of  the  nursery. 

From  Prof.  R.  P.  Dunn,  Brown  University. 

1  had  already  determined  to  adopt  it  as  the  principal 
book  of  reference  in  my  department.  This  is  the  first 
term  in  which  it  has  been  used  here;  but  from  the  trial 
which  I  have  now  made  of  it,  I  have  every  reason  to 
congratulate  myself  on  my  selection  of  it  as  a  text- 
book. 


From  A.  B.  Davenport,  Esq ,  Brooklyn  N.  Y. 
The  work  of  Shaw  and  Tuekerman  on  English  and 
American  literature  particularly  interested  me.  It  is 
truly  a  mullum  in  parvo.  I  know  not  where  one  can 
find  so  much  information  condensed  upon  the  topics 
on  which  it  treats  as  is  to  be  found  in  this  work. 
Either  as  a  text  book,  or  for  higher  classes  in  read- 
ing, it  is  worthy  of  general  adoption. 

From  Prof.  J.  Munroe,  Oberlin  College. 
I  have  examined  it  carefully,  and  value  it  highly, 
It  fills  a  place  not  occupied  by  any  other  book  with 
which  I  am  acquainted.  It  will  probably  be  intro- 
duced in  this  institution  as  a  text-book  preparatory  to 
the  study  of  English  literature. 

From  Report  of  the  Teachers'1  Association  of  Lauder- 

dale  County,  Ga. 

A  careful  perusal  of  the  "Outlines  of  English  Lite- 
rature," by  Professor  Shaw,  of  St.  Petersburg,  has 


afforded  us  great  pleasure 
in  the  hands  of  the  student 


It  is  designed  to  place 
Manual,  that,  without 


being  too  voluminous,  shall  impart  a  general  and 
correct  knowledge  upon  a  subject  that  ought  to  be 
f  imiliar  to  all  who  use  the  noble  old  English  tongue. 
By  its  aid,  the  scholar  will  learn  how  our  language, 
springing  from  the  original  Saxon,  by  an  admixture 
of  Norman  French,  and  finally  of  the  Latin  and 
Greek,  has  arrived  at  its  present  high  state  of  perfec- 
tion. He  will  also  become  well  acquainted  with  the 
most  celebrated  writers  of  England  during  the  dif- 
ferent periods  of  her  literary  history,  their  lives,  their 
characters,  and  their  writings.  We  hope  it  will  be 
extensively  used. 


BROWNE'S  CLASSICAL  LITERATURE— (Now  Complete.) 

A  HISTORY  OF  GREEK  CLASSICAL  LITERATURE. 

BY  THE  REV.  R.  W.  BROWNE,  M.  A., 

Professor  of  Classical  Literature  in  King's  College,  London. 
In  one  very  handsome  crown  octavo  volume.    $1  50. 

By  tlie  same  Author,  to  matcli— (Now  Ready.) 

A  HISTORY  OF  ROMAN  "CLASSICAL  LITERATURE. 

In  one  very  handsome  crown  octavo  volume.     $1  50. 

From  Prof.  Gessner  Harrison,  University  of  Va. 


I  am  very  favorably  impressed  with  the  work  from 
what  I  have  seen  of  it,  and  hope  to  find  in  it  an  im- 
portant help  for  my  class  of  history.  Such  a  work  is 
very  much  needed. 

From  Prof.  J.  A.  Spencer,  New  York. 
It  is  an  admirable  volume,  sufficiently  full  and  co- 
pious in  detail,  clear  and  precise  in  style,  very  scholar- 
like  in  its  execution,  genial  in  its  criticism,  and  alto- 
gether displaying  a  mind  well  stored  with  the  learning, 
genius,  wisdom,  and  exquisite  taste  of  the  ancient 
Greeks.  It  is  in  advance  of  everything  we  have,  and 
it  may  be  considered  indispensable  to  the  classical 
scholar  and  student. 


Mr.  Browne's  present  publication  has  great  merit. 
His  selection  of  materials  is  judiciously  adapted  to  the 
purpose  of  conveying  within  a  moderate  compass 
some  definite  idea  of  the  leading  characteristics  of 
the  great  classical  authors  and  their  works.  *  *  **  Mr. 
Browne  has  the  happy  art  of  conveying  information 
in  a  most  agreeable  manner.  It  is  impossible  to  miss 
his  meaning,  or  be  insensible  to  the  charms  of  his  po- 
lished style.  Suffice  it  to  say,  that  he  has,  in  a  very 
readable  volume,  presented  much  that  is  useful  to  Ihe 
classical  reader.  Besides  biographical  information 
in  reference  to  all  the  classical  Greek  authors,  he  has 
furnished  critical  remarks  on  their  intellectual  pecu- 
liarities, and  an  analysis  of  their  works  when  they 
are  of  sufficient  importance  to  deserve  it.— London 
Athenceum. 


BLANCHARD  &  LEA'S    EDUCATIONAL    PUBLICATIONS. 


HBRSCHEL'S  ASTRONOMY. 

OUTLINES  OF~ASTRONOMY. 

BY  SIR  JOHN  F.  W.  HERSCHEL,  BART.,  F.R.  S.,  &c. 

A  NEW  AMERICAN,  FROM  THE  FOURTH  AND  REVISED  LONDON  EDITION. 

In  one  handsome  crown  octavo  volume,  with  numerous  plates  and  wood-cuts. 

Extra  cloth,  $1  60 ;  or,  half  bound,  leather  backs  and  cloth  sides,  $1  75. 

The  present  work  is  reprinted  from  the  last  London  edition,  which  was  carefully  revised  by 
the  author,  and  in  which  he  embodies  the  latest  investigations  and  discoveries.  It  may  therefore 
be  regarded  as  fully  on  a  level  with  the  most  advanced  state  of  the  science,  and  even  better 
adapted  than  its  predecessors,  as  a  full  and  reliable  text-book  for  advanced  classes.  • 

A  few  commendatory  notices  are  subjoined,  from  among  a  large  number  with  which  the  pub- 
lishers have  been  favored. 

Astronomy  in  all  our  institutions,  except  perhaps 
those  where  it  is  studied  mathematically. 


From  Professor  D.  Olmstead,  Yale  College. 
A  rich  mine  of  all  that  is  most  valuable  in  modern 
Astronomy. 

From  Prof.  A.  Caswtll,  Brown  University,  R.  I. 
As  a  work  of  reference  and  study  for  the  more  ad- 
vanced pupils,  who  yet  are  not  prepared  to  avail 
themselves  of  the  higher  mathematics,  I  know  of  no 
work  to  be  compared  with  it. 

From  Prof.  Samuel  Jones,  Jefferson  College,  Pa., 
May  28,  1853. 

This  treatise  is  too  well  known,  and  too  highly  ap- 
preciated in  the  scientific  world  to  need  new  praise. 
A  distinguishing  merit  in  this,  as  in  the  other  produc- 
tions of  the  author,  is  that  the  language  in  which  the 
profound  reasonings  of  science  are  conveyed  is  so 
perspicuous  that  the  writer's  meaning  can  never  be 
misunderstood. 

From  Prof.  J.  F.  Crorker,  Madison  College,  Pa, 
May  17,  1S53. 

I  know  no  treatise  on  Astronomy  comparable  1o 
"  Herschel's  Outlines."  It  is  admirably  adapted  to 
the  necessities  of  the  student.  We  have  adopted  it 
as  a  text- book  in  our  College. 

From  Prof.  James  Curley,  Georgetown  College, 

May  s>4,  1853. 

As  far  as  I  am  able  to  judge,  it  is  the  best  work  of 
its  class  in  any  language. 

From  Prof.  N.  TilHnghast,  Bridgewater,  Mass., 

May  12,  1853. 

It  would  not  become  me  to  speak  of  the  scientific 
merits  of  such  a  work  by  such  an  author;  but  I  may- 
be allowed  jo  say.  that  I  most  earnestly  wish  that  it 
might  supersede  every  book  used  as  a  text-book  on 


We  now  take  leave  of  this  remarkable  work,  which 
we  hold  to  be,  beyond  a  doubt,  the  greatest  and  most 
remarkable  of  the  works  in  which  ihe  laws  of  astro- 
nomy and  the  appearance  of  the  heavens  are  de- 
scribed to  those  who  are  not  mathematicians  nor 
observers,  and  recalled  to  those  who  are.  It  is  the 
reward  of  men  who  can  descend  fr»>m  the  advance- 
ment of  knowledge,  to  care  for  its  diffusion,  that  their 
works  are  essential  to  all,  that  they  become  the 
manuals  of  the  proficient  aswell  as  the  lexl-books'of 
the  learner. — AthencEum. 

There  is,  perhaps,  no  book  in  the  English  language 
on  the  subject,  which,  whilst  it  contains  so  many  of 
the  facts  of  Astronomy  (which  it  attempts  to  explain 
with  as  little  technical  language  as  possible),  is  so  at- 
tractive in  its  style,  and  so  clear  and  forcible  in  its 
illustrations.—  Evangelical  Review. 

Probably  no  book  ever  written  upon  any  science, 
embraces  within  so  small  a  compass  an  entire  epitome 
of  everything  known  within  all  its  various  depart- 
ments, practical,  theoretical,  and  physical.  —  Ex- 
aminer. 

There  is  not,  perhaps,  in  the  English  language,  a 
work,  treating  upon  so  abstruse  a  subject,  certainly 
not  upon  Astronomy,  written  with  so  much  concise- 
ness and  explicitness,  and  yet  in  so  easy  and  intelli- 
gible a  style,  with  such  an  avoidance  of  technicali- 
ties, and  which  one  that  is  not  an  adept  in  the  science 
can  read  so  understandingly.  The  very  learned  au- 
thor has  done  almost  as  much  for  the  cause  of  Astro- 
nomy by  the  preparation  of  this  work,  by  which  the 
knowledge  of  it  will  be  diffused  among  the  people,  as 
by  his  wonderful  discoveries.— N.  Y.  Observer. 


NEW  PHYSIOLOGICAL  TEXT-BOOK— (Now  Ready.) 

PHYSIOLOGY  OF  ANIMAL" AND  VEGETABLE  LIFE. 

A   POPULAR  TREATISE 
ON   THE   PHENOMENA   AND   FUNCTIONS   OP   ORGANIC   LIFE. 

To  which  is  Prefixed  a  Brief  General  View  of  the  Great  Departments  of  Human  Knowledge, 

In  one  handsome  royal  12mo.  volume,  of  234  pages,  with  over  100  handsome  illustrations. 
Written  by  a  man  of  Science,  this  work,  though  popular  in  its  form  and  elementary  in  its  teach- 
ings, avoids  the  objections  usually  urged  against  similar  treatises,  ofsuperficiahty  and  incorrectness. 
While  its  language  and  arrangement  are  such  as  to   render  it  easily  understood  by  the  youthful 
student  or  general  reader,  its  basis  is  strictly  scientific,  and  on  every  point  it  will  1 
level  with  the  most  advanced  state  of  knowledge. 


BIRD'S  NATURAL  PHILOSOPHY. 

ELEMENTS  OF  NATURAL  PHILOSOPHY  fbeing  an  Experimental  Introduction  to  the  Phy- 
sical   Sciences.     Illustrated  with   over    300   wood-cuts.     By  GOLDING   BIRD,  M.  D.,  Assisi 
Physician  to  Guy's  Hospital.   From  the  Third  London  edition.   In  one  neat  volume,  royal  1. 
extra  cloth,  $1  25;  strong  leather,  $1  50. 

lish  language  of  this  wide  range  of  physical  subjects. 


We  are  astonished  to  find  that  there  is  room  in  so 
small  a  bonk  for  even  the  bare  recital  of  so  many 
subjects.  Where  everything  is  treated  succinctly, 
sjreat  judgment  and  much  lime  are  needed  in  making 
a  selection  and  winnowing  the  wheat  from  the  chaff. 
Dr.  Bird  has  no  need 'to  plead  the  peculiarity  of 
his  position  as  a  shield  against  criticism,  so  lon»  as 
his  book  continues  to  be  the  bejst  epitome  in  the  Eng- 


— North  American  Review. 

From  Prof.  John  Johnston,  Wesley  an  Univ., 

Middletown,  Ct. 

For  those  desiring  as  extensive  a  work,  I  think  it 
decidedly  superior  to  anything  of  the  kind  with  which 
I  am  acquainted. 


10 


BLANCHARD  &  LEA'S    SCIENTIFIC  PUBLICATIONS. 


CARPENTER'S    COMPARATIVE    PHYSIOLOGY. 
New  and.  Improved  Edition—  Now  Ready. 

PRINCIPLES  OF 

COMPARATIVE   PHYSIOLOGY. 

BY  WILLIAM  B.  CARPENTER,  M.  D.; 

Author  of  "  Principles  of  Human  Physiology,"  &c. 
A  new  American  edition,  revised  and  improved  by  the  author. 

WITH  OVER  THREE  HUNDRED  ILLUSTRATIONS. 

In  one  large  and  very  handsome  octavo  volume,  of  750  pages. 

The  delay  which  has  existed  in  the  appearance  of  this  work  has  been  caused  by  the  very  thorough 
revision  and  remodelling  which  it  has  undergone  at  the  hands  of  the  author,  and  the  large  numbei 
of  new  illustrations  which  have  been  prepared  for  it.  It  will,  therefore,  be  found  almost  a  new 
work,  and  fully  up  to  the  day  in  every  department  of  the  subject,  rendering  it  a  reliable  text-booh 
for  all  students  engaged  in  this  branch  of  science.  Every  effort  has  been  made  to  render  its  typo- 
graphical finish  and  mechanical  execution  worthy  of  its  exalted  reputation,  and  creditable  to  the 
mechanical  arts  of  this  country. 


This  work  stands  without  its  fellow.  It  is  one  few 
men  in  Europe  could  have  undertaken;  it  is  one,  no 
man,  we  believe,  could  have  brought  to  so  success- 
ful an  issue  as  Dr.  Carpenter.  VVe  feel  that  this 
abstract  can  give  the  reader  a  very  imperfect  idea  of 
the  fulness  of  this  work,  and  no  idea  of  its  unity,  of 
the  admirable  manner  in  which  material  has  been 


brought,  from  the  most  various  sources,  to  conduce  u 
its  completeness,  of  the  lucidity  of  the  reasoning  i 
contains,  or  of  the  clearness  of  language  in  which  the 
whole  is  clothed.  Not  the  profession  only,  but  thf 
scientific  world  at  large,  must  feel  deeply  indebted  tc 
Dr.  Carpenter  for  this  great  work.  It  must,  indeed 
add  largely  even  to  his  high  reputation. — Med.  Times 


JOHNSTON'S    PHYSICAL    ATLAS. 

THE  PHYSICAL  ATLAS  OF  NATURAL  PHENOMENA, 

FOR  THE  USE  OF  COLLEGES,  ACADEMIES,  AND  FAMILIES. 
BY  ALEXANDER  KEITH  JOHNSTON,  F.  R.  a.  S.;  &c. 

In  one  large  imperial  4to.  volume,  strongly  bound  in  half  morocco. 

With  Twenty-six  Plates,  Engraved  and  Colored  in  the  best  style, 

Together  with  over  one  hundred  pages  of  Descriptive  Letterpress,  and  a  very  copious  Index, 

Price  $12  00. 


The  book  before  us  is,  in  short,  a  graphic  encyclo- 
paedia of  the  sciences — an  atlas  of  human  knowledge 
done  into  maps.  It  exemplifies  the  truth  which  it  ex- 
presses— that  he  who  runs  may  read.  The  Thermal 
Laws  of  Leslie  it  enunciates  by  a  bent  line  running 
across  a  map  of  Europe  ;  the  abstract  researches  of 
Gauss  it  embodies  in  a  few  parallel  curves  winding 
over  a  section  of  the  globe  ;  a  formula  of  Laplace  it 
melts  down  to  a  little  patch  of  mezzotint  shadow;  a 
problem  of  the  transcendental  analysis,  which  covers 
pages  with  definite  integrals,  it  makes  plain  to  the  eye 
by  a  little  stippling  and  hatching  on  a  given  degree  of 
longitude  !  All  possible  relations  of  time  and  space, 
heat  and  cold,  wet  and  dry,  frost  and  snow,  volcano 
and  storm,  current  and  tide,  plant  and  beast,  race  and 
religion,  attraction  and  repulsion,  glacier  and  ava- 


lanche, fossil  and  mammoth,  river  and  mountain, 
mine  and  forest,  air  and  cloud,  and  sea  and  sky— all 
in  the  earth  and  under  the  earth,  and  on  the  earth, 
and  above  the  earth,  that  the  heart  of  man  has  con- 
ceived or  his  head  understood— are  brought  together 
by  a  marvellous  microcosm,  and  planted  on  these 
little  sheets  of  paper,  thus  making  themselves  clear 
to  every  eye.  In  short,  we  have  a  summary  of  all 
the  cross-questions  of  Nature  for  twenty  centuries— 
and  all  the  answers  of  Nature  herself  set  down  and 

speaking  to  us  voluminous  system  dansun  mot 

Mr.  Johnston  is  well  known  as  a  geographer  of  great 
accuracy  and  research  ;  and  it  is  certain  that  this 
work  will  add  to  his  reputation;  for  it  is  beautifully 
engraved,  and  accompanied  with  explanatory  and 
tabular  letterpress  of  great  value.— AlhencBum. 


CHEMICAL  TEXT-BOOK  FOR  STUDENTS- (Just  Issued.) 

ELEMENTARY"  CHEMISTRY, 

THEORETICAL    AND    PRACTICAL. 

BY  GEORGE  FOWNES,  PH.D.,  &c. 
WITH    NUMEROUS    ILLUSTRATIONS. 

A    NEW   AMERICAN,  FROM   THE   LAST   AND   REVISED  LONDON  EDITION.      EDITED,  WITH  ADDITIONS, 

BY  ROBERT   BRIDGES,  M.  D. 

In  one  large  royal  12mo.  volume,  containing  over  550  pages,  clearly  printed  on  small  type,  with 

181  illustrations  on  wood  ;  extra  cloth,  $1  35;  strong  leather,  $1  50. 
We  know  of  no  better  text-book,  especially  in  the 


difficult  department  of  organic  chemistry,  upon  which 
it  is  particularly  full  and  satisfactory.  We  would 
recommend  it  to  preceptors  as  a  capital  "  office  book" 
for  their  students  who  are  beginners  in  Chemistry. 
It  is  copiously  illustrated  with  excellent  wood-cuts, 
and  altogether  admirably  "got  up."—  N.  J.  Medical 
Reporter,  March,  1554. 

A  standard  manual,  which  has  long  enjoyed  the 
reputation  of  embodying  much  knowledse  in  a  small 


condensation  with  masterly  tact.  His  book  is  con- 
cise without  being  dry,  and  brief  without  being  too 
dogmatical  or  general.—  Virginia  Med.  and  Surgical 
Journal. 

The  work  of  Dr.  Fownes  has  long  been  before  the 
public,  and  its  merits  have  been  fully  appreciated  as 
the  best  text-book  on  Chemistry  now  in  existence. 
We  do  not,  of  course,  place  it  in  a  rank  superior  to 
the  works  of  Brande,  Graham,  Turner.  Gregory,  or 
Gmelin,  but  we  say  that,  as  a  work  for  students, it  is 


space.    The  author  has  achieved  the  difficult  task  of  J  preferable  to  any  of  them. — Lond.  Journal  of  Medicine, 


BLA.NCHARD    &   LEA'S    SCIENTIFIC    PUBLICATIONS.  11 

NOW    READY. 

HANDBOOK  OF  CHEMISTRY,  Theoretical,  Practical,  and  Technical.  By  A.  F  ABEL  F  C  S~  and  C 
L.  BLOXAM.  With  a  Recommendatory  Preface  by  Dr.  HOFMANN,  and  numerous  illustrations  on  wood  In 
one  large  and  handsome  octavo  volume,  of  662  pages,  extra  cloth,  $3  25. 

It  must  be  understood  that  this  is  a  work  fitted  for  the  earnest  student,  who  resolves  to  pursue  for  himself 
a  steady  search  into  the  chemical  mysteries  of  creation.  For  such  a  student  the  "  Handbook"  will  prove  an 
excellent  guide,  since  he  will  find  in  it,  not  merely  the  most  approved  modes  of  analytical  investigation  but 
descriptions  of  the  apparatus  necessary,  with  such  manipulatory  details  as  rendered  Faraday's  "Chemical 
Manipulations"  so  valuable  at  the  time  of  its  publication.  Beyond  this,  the  importance  of  the  work  is  in- 
creased by  the  introduction  of  much  of  the  technical  chemistry  of  the  manufactory. — Athenaum. 

THE    PRINCIPAL    FORMS    OF    THE    SKELETON, 

AND  THE  FORMS  AND  STRUCTURE  OF  THE  TEETH.  By  PROFESSOR  R.  OWEN.  In  one  very 
handsome  royal  12mo.  volume,  with  numerous  illustrations  on  wood.  (Just  Ready.) 

This  volume  will  present  in  a  concise  and  popular  form  a  complete  view  of  the  most  recent  state  of  com- 
parative osteology;  the  correctness  of  which  is  sufficiently  vouched  for  by  the  name  of  the  distinguished 
author.  A  subject  of  so  much  interest  to  the  man  of  science,  and  more  especially  to  the  geologist,  cannot 
fail  to  attract  general  attention.  

TECHNOLOGY; 

OR,  CHEMISTRY  APPLIED  TO  THE  ARTS  AND  TO  MANUFACTURES.  By  Dr.  F.  KNAPP.  Edit- 
ed, with  numerous  Notes  and  Additions,  by  Dr.  EDMUND  RONALDS  and  Dr.  THOMAS  RICHARDSON.  With 
additional  Notes  by  Prof.  WALTER  R.  JOHNSON.  In  two  large  and  very  handsome  octavo  volumes,  with 
about  five  hundred  splendid  illustrations.  $6  00. 

PRINCIPLES  ~OF    THE    MECHANICS 

OF  MACHINERY  AND  ENGINEERING.  By  Prof.  JULIUS  WEISBACH.  Translated  and  edited  by  Prof. 
GORDON,  of  Glasgow.  With  Addition?,  by  Prof.  WALTER  R.  JOHNSON.  In  two  large  and  very  handsome 
octavo  volumes,  with  about  one  thousand  beautiful  illustrations.  $6  50. 


CARPENTER   ON    ALCOHOL-(NOW    READY.) 
ON  THE  USE  AND  ABUSE  OF  ALCOHOLIC  LIQUORS  IN  HEALTH  AND  DISEASE.    By  W.  B. 

CARPENTER,  M.  D.,  author  of  "  Human  Physiology,"  &c.    New  edition,  with  Preface  and  Notes,  by  D.  F. 

CONIHE,  M.  D.    In  one  neat  royal  12mo.  volume,  extra  cloth. 

This  new  edition  has  been  prepared  with  a  view  to  an  extended  popular  circulation  of  this  valuable  work, 
the  notes  by  Dr.  Condie  containing  explanations  of  the  scientific  terms  employed.  Copies  in  flexible  cloth 
may  be  had  free  of  postage  by  mail  on  remitting  50  cents  to  the  publishers. 

A  very  liberal  deduction  will  be  made  when  quantities  are  taken  for  distribution  by  societies  or  individuals. 

DE    LA    BECHE'S    GEOLOGY. 

THE  GEOLOGICAL  OBSERVER.    By  Sir  HENRY  T.  DE  LA  BECHE,  C.  B.,  F.  R.  S  ,  Director-General  of  the 
Geological  Survey  of  Great  Britain.    In  one  large  and  handsome  octavo  volume,  extra  cloth,  of  seven 
hundred  pages,  with  over  three  hundred  wood-cuts.    $3  50. 
This  volume  will  be  found  to  present  a  very  complete  summary  of  what  has  already  been  accomplished 

in  the  science  of  geology,vwhile  at  the  same  time  it  indicates  to  the  student  the  mode  and  direction  in  which 

future  researches  should  be  pursued. 


BONAPARTE'S  AMERICAN   ORNITHOLOGY.     In  four  handsome  quarto  volumes,  with  large  and 

splendid  colored  plates.    $25  00. 

BRODERIP'S  ZOOLOGICAL  RECREATIONS.    In  one  neat  royal  12mo.  volume,  extra  cloth,  75  cents. 
BOWMAN'S  HANDBOOK  OF  PRACTICAL  CHEMISTRY,  including  Analysis.     In  one  neat  royal 

J2mo.  volume,  extra  cloth,  with  numerous  illustrations.    $1  20. 
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from  an  old  Practitioner  to  a  Patient.    In  one  neat  royal  12mo.  volume,  extra  cloth,  bO      nts. 
GRIFFITH'S  CHEMISTRY  OF  THE  FOUR  SEASONS,  SPRING,  SUMMER,  AUTUMN,  AND  WINTER.    In 

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POPULAR    PHYSIOLOGY 

OF  ANIMAL  AND  VEGETABLE  LIFE.    In  one  handsome  royal  12mo.  volume  of  200  pages,  with  over 
100  engravings  on  wood.    (Now  Ready.)    See  P.  9. 

PHYSICAL    GEOGRAPHY. 

Bv  MART  SOMERVILLE.    A  new  American,  from  the  last  and  Revised  London  E.  Ih^r 

Glossary,  by  W.  S.  W.  RUSCHENBERGER,  M.  D.,  U.  S.  N.  In  one  large  royal  12mo.  volume,  extra  cloth 
(See  P.I.) 


DANA  ON  ZOOPHYTES  AND  CORALS.    Being  a  portion  of  the  ^^^lil^SSt  i 

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colored  plates,  handsomely  and  strongly  bound  in  half  morocco,  »4  •  OU. 
EVANS'S  YOUNG  MILLWRIGHT'S  AND  MILLER'S  GUIDE.  Fourteenth  Edition.  E 

P.  JONES.    In  one  octavo  volume,  leather,  with  numerous  plates,  82  50. 
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royal  12mo.  volume,  extra  cloth,  $1  00.  .  ~*Tm  ™  T-»T  \  T>r-c 

HUMBOLDT'S  ASPECTS  OF  NATURE  IN  DIFFERENT  LANDS  AND  DIFFERENT  CLIMATE 

Translated  by  MRS.  SABINE.    In  one  large  royal  12mo.  volume,  extra  ciotli,  «H  ~WT~~  ^v«v 

HALE'S  ETHNOGRAPHY  AND   PHILOLOGY  OF   THE  UNITED   STATES  EXPLORING  EXPL- 

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of  2000  pages,  with  1000  illustrations.    $5  00.    H7"  See  P.  2. 
SCHCEDLER'S  BOOK  OF  NATURE.    A  Popular  Introduction  to  the  f  Sciences  i  of  ^u«'occ 

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with  nearly  700  illustrations.    $>L  80.     ffcj*  See  P.  2. 
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half  bound  in  morocco,  with  26  colored  plates.    $12  00.    LLT  feee  f.  iu. 


12       BLANCHARD  &  LEA'S   MISCELLANEOUS  PUBLICATIONS. 
COMPLETE    LIBRARY    EDITION. 

LIYES  OF  THE  QUEENS  OF  ENGLAND, 

FROM  THE   NORMAN  CONQUEST: 

WITH  ANECDOTES  OF  THEIR  COURTS. 

Now  first  published  from  Official  Records,  and  other  Authentic  Documents,  Private  as  ivell  as  Public. 
NEW  EDITION,  WITH  ADDITIONS  AND  CORRECTIONS. 

BY  AGNES  STRICKLAND. 

Complete  in  six  very  handsome  crown  octavo  volumes,  containing  over  THIRTY-SIX  HUNDRED 
PAGES,  and  for  sale  in  various  styles  of  binding,  at  very  reasonable  prices. 

The  publishers  have  great  pleasure  in  presenting  to  the  public  this  work  in  a  complete  form. 
During  the  long  period  in  which  it  has  been  issuing  from  the  press,  it  has  assumed  the  character 
of  a  standard  work,  and  as  occupying  ground  hitherto  untouched;  as  embodying  numerous  his- 
torical facts  heretofore  unnoticed,  and  as  containing  vivid  sketches  of  the  characters  and  manners 
of  the  times,  with  anecdotes,  documents,  &c.  &c.,  it  presents  numerous  claims  on  the  attention 
of  both  the  student  of  history  and  the  desultory  reader. 

A  valuable  contribution  to  historical  knowledge. 
It  contains  a  mass  of  every  kind  of  historical  matter 
of  interest,  which  industry  and  research  could  col- 
lect. We  have  derived  much  entertainment  and  in- 
struction from  the  work. — Atheiuzum. 

This  interesting  and  well-written  work,  in  which 


the  severe  truth  of  history  takes  almost  the  wild- 
ness  of  romance,  will  constitute  a  valuable  addition 
to  our  biographical  literature. — Morning  Herald. 

These  volumes  have  the  fascination  of  a  romance 
united  to  the  integrity  of  history. — Times. 


Also,  to  be  had  separate, 

STRICKLAND'S  LIVES  OF  THE  QUEENS  OF  HENRY  VIII.,  and  of  his  Mother,  ELIZA- 
BETH OF  YORK.  Complete  in  one  very  neat  crown  octavo  volume,  extra  cloth,  of  over  four 
hundred  pages. 

STRICKLAND'S  MEMOIRS  OF  ELIZABETH,  Second  Queen  Regnant  of  England  and  Ireland. 
Complete  in  one  very  neat  crown  octavo  volume,  extra  cloth,  of  nearly  six  hundred  pages. 


ROMANTIC    HISTORY   OF   THE    HUGUENOTS. 

HISTORY  OF  THE  PROTESTANT  REFORMATION  IN  FRANCE.     By  MRS.  MASSH,  author 
of  "Two  Old  Men's  Tales,"  &c.     In  two  very  handsome  royal  12mo.  volumes,  extra  cloth. 


PULSZKY'S  MEMOIRS  OF  AN    HUNGARIAN    LADY.     In  one  neat  royal    12mo.   volume, 
extra  cloth. 

PARDOE'S  COURT  AND  TIMES  OF  FRANCIS  I.,  KING  OF  FRANCE.     In  two  handsome 
royal  12mo.  volumes,  extra  cloth. 

LORD  HERVEY'S  MEMOIRS  OF  THE  COURT  OF  GEORGE  II.     In  two  neat  royal  12mo. 
volumes,  extra  cloth. 


RUSSEL'S  LIFE  OF  FOX— (Just  Issued.) 

MEMORIALS   AND    CORRESPONDENCE  OF 

CHARLES  JAMES  FOX. 

EDITED  BY  THE  ET.  HON.  LORD  JOHN  RUSSEL,  M.  P. 

In  two  handsome  royal  12mo.  volumes,  extra  cloth. 


The  work  is  deeply  interesting,  as  it  throws  light 
upon  ihe  career  of  a  great  man,  and  reveals  the  pri- 
vate sentiments  of  many  eminent  British  statesmen 
in  regard  to  our  revolutionary  struggle,  and  in  regard 
to  the  wars  waged  against  the  French  Republic. 
The  correspondence  presents  Mr.  Fox  in  the  attitude 
of  a  friend  to  the  colonies,  not  only  on  general  prin- 
ciples, but  as  one  whose  feelings  were  strongly  en- 


listed in  their  cause.  There  are  occasional  letters  in 
these  volumes,  which,  if  they  had  fallen  into  the 
hands  of  the  British  government  at  that  time,  would 
probably  have  caused  the  author  some  trouble,  though 
it  was  a  period  when  party  spirit  ran  very  high, 
and  state?  men  took  the  largest  license.—  N.  Y.  Com- 
mercial Advertiser. 


BLANCHARD  &  LEA'S   MISCELLANEOUS   PUBLICATIONS.      13 
Campbell's  Chancellors  and  Chief  Justices. 

LIVES  OF  THE   LORD  CHANCELLORS 

Keqjtrs  of  tlje  ®rmt  6ml  of 


FROM 

THE  EARLIEST  TIMES  TO  THE  REIGN  OF  KING  GEORGE  IV. 
BY  LORD  CHIEF-JUSTICE  CAMPBELL,  A.M.,  F.  R.  S.  E. 

Second  American,  from  the  Third  London  edition, 

COMPLETE  IN  SEVEN  HANDSOME  CROWN  OCTAVO  VOLUMES,  EXTRA  CLOTH,  OR  HALF  MOROCCO. 
ALSO,   TO  MATCH. 

LIVES  OF  THE  CHIEF-JUSTICES  OF  ENGLAND, 

From  the  Norman  Conquest  to  the  Death  of  Lord  Mansfield, 

Second  Edition. 

In  two  very  neat  volumes,  crown  octavo,  extra  cloth,  or  half  morocco. 
Of  the  solid  merit  of  the  work  our  judgment  may  be 


gathered  from  what  has  already  been  said.  We  will 
add,  that  from  its  infinite  fund  of  anecdote,  and  happy 
variety  of  style,  the  book  addresses  itself  with  equal 
claims  to  the  mere  general  reader,  as  to  the  legal  or 
historical  inquirer ;  and  while  we  avoid  the  stereo- 
typed commonplace  of  affirming  that  no  library  can 
be  complete  without  it.  we  feel  constrained  to  afford  it 
a  higher  tribute  by  pronouncing  it  entitled  to  a  distin- 
guished place  on  the  shelves  of  every  scholar  who 
is  fortunate  enough  to  possess  it.— Frazer's  Magazine. 


A  work  which  will  take  its  place  in  our  libraries 
as  one  of  the  most  brilliant  and  valuable  contribu- 
tions to  the  literature  of  the  present  day. — Athenaum 

The  brilliant  success  of  this  work  in  England  is  by 
no  means  greater  than  its  merits.  It  is  certainly  the 
most  brilliant  contribution  to  English  history  made 
within  our  recollection;  it  has  the  charm  and  free- 
dom of  Biography  combined  with  the  elaborate  and 
careful  comprehensiveness  of  History. — N.  Y.  Tri- 
bune. 


ON    THE    LAW    OF   CONTRACTS, 

AND  ON  PARTIES  TO  ACTION  EX  CONTRACTS.    By  C.  G.  ADDISON,  of  the  Inner  Temple, 
Barrister  at  Law.     In  one  large  and  handsome  octavo  volume. 


A    NEW    LAW    DICTIONARY, 

Containing  Explanations  of  such  Technical  Terms  and  Phrases  as  occur  in  the  works  of  Legal 
Authors,  in  the  Practice  of  the  Courts,  and  in  the  Parliamentary  Proceedings  of  the  Houses  of 
Lords  arid  Commons.  To  which  is  added  an  Outline  of  an  Action  at  Law,  and  of  a  Suit  in 
Equity.  By  HENRY  JAMES  HOLTHOUSE,  Esq.  Edited,  from  the  second  and  enlarged  English 
edition,  with  numerous  Additions,  by  HENRY  PENINGTON,  of  the  Philadelphia  Bar.  In  one 
large  royal  12mo.  volume,  of  five  hundred  double-columned  pages. 


TURKEY    AND    ITS    DESTINY. 
BY    CHARLES    MACFARLANE,    ESQ. 

In  two  neat  royal  12mo.  volumes,  extra  cloth. 


NIEBTTHR'S  ANCIENT  HISTORY. 

LECTURES  ON  ANCIENT  HISTORY: 

COMPRISING 

The  History  of  the  Asiatic  Nations,  the  Egyptians,  Greeks,  Macedonians,  and  Carthaginians, 
BY  B.  G.   NIEBUHK. 

TRANSLATED  FROM  THE  GERMAN,  BY  DR.  L.  SCHMITZ, 

WITH  ADDITIONS  FROM  MSS.  IN  THE  EXCLUSIVE  POSSESSION  OF  THE  EDITOR. 

In  three  very  handsome  crown  octavo  volumes,  extra  cloth. 

The  extraordinary  familiarity  of  Niebuhr  with  the  literatures  of  all  nations,  his  profound  know- 
ledge  of  all  political  and  human  affairs,  derived  not  only  from  books,  but  from  practical  life,  and 
his  brilliant  powers  of  combination,  present  to  us  in  these  Lectures,  as  in  those  on  Roman  history, 
such  an  abundance  of  new  ideas,  startling  conceptions  and  opinions,  as  are  rarely  to  be  met  with 
in  any  other  work.  They  are  of  the  highest  importance  and  interest  to  all  who  are  engaged  in 
the  study,  not  only  of  antiquity,  but  of  any  period  in  the  history  of  man. 


14       BLANCHARD  &   LEA'S  MISCELLANEOUS    PUBLICATIONS. 


NARRATIVE  OF  THE  UNITED  STATES  EXPEDITION 

TO  THE  DEAD  SEA  AtfD  RIVER  JORDAN. 

BY  W.   F.  LYNCH,  U.S.N., 

Commander  of  the  Expedition. 
In  one  very  large  and  handsome  octavo  volume  with  twenty-eight  beautiful  plates,  and  two  maps. 


This  book,  so  long  and  .anxiously  expected,  fully 
sustains  the  hopes  of  the  most  sanguine  and  fastidious 
It  is  truly  a  magnificent  work.  The  type,  paper, 
binding,  style,  and  execution,  are  all  of  the  best  and 
highest  character,  as  are  also  the  maps  and  engrav- 
ings. It  will  do  more  to  elevate  the  character  of 


our  national  literature  than  any  work  that  has  ap- 
peared for  years.  The  intrinsic  interest  of  the  sub- 
ject will  give  it  popularity  and  immortality  at  once. 
It  must  be  read  to  be  appreciated;  and  it  will  be 
read  extensively,  and  valued,  both  in  this  and  other 
countries. — Lady^s  Book. 


Also,  to  be  had — 

CONDENSED  EDITION,  in  one  neat  royal  12mo.  volume,  extra  cloth,  with  a  map. 


MEMOIRS  OF  THE  LIFE  OF  WILLIAM  WIBT. 

BY  THE  HON.  JOHN  P.  KENNEDY. 

SECOND    EDITION,    REVISED. 
WITH  A  PORTRAIT,  AND  FAC-SIMILE  OF  A  LETTER  FROM  JOHN  ADAMS. 

In  two  large  and  handsome  royal  12mo.  volumes,  extra  cloth. 

In  its  present  neat  and  convenient  form,  the  work  is  eminently  fitted  to  assume  the  position 
which  it  merits  as  a  book  for  every  parlor-table  and  for  every  fireside  where  there  is  an  appre- 
ciation of  the  kindliness  and  manliness,  the  intellect  and  the  affection,  the  wit  and  liveliness 
which  rendered  William  Wirt  at  once  so  eminent  in  the  world,  so  brilliant  in  society,  and  so 
loving  and  loved  in  the  retirement  of  his  domestic  circle.  Uniting  all  these  attractions,  it  cannot 
fail  to  find  a  place  in  every  private  and  public  library,  and  in  all  collections  of  books  for  the  use  of 
schools  and  colleges,  for  the  young  can  have  before  them  no  brighter  example  of  what  can  be  ac- 
complished by  industry  and  resolution,  than  the  life  of  William  Wirt,  as  unconsciously  related  by 
himself  in  these  volumes. 

DON  QUIXOTE  DE  LA  MANCIIA.  Translated  from  the  Spanish  of  Miguel  de  Cervantes 
Saavedra,  by  CHARLES  JARVIS,  Esq.  Carefully  revised  and  corrected,  with  a  Memoir  of  the  Au- 
thor and  a  notice  of  his  works.  With  numerous  illustrations,  by  Tony  Johannot.  In  two  beau- 
tifully printed  volumes,  crown  octavo,  various  styles  of  binding. 

The  handsome  execution  of  this  work,  the  numerous  spirited  illustrations  with  which  it  abounds,  and  the 
very  low  price  at  which  it  is  offered,  render  it  a  most  desirable  library  edition  for  all  admirers  of  the  immorta, 
Cervantes. 

NARRATIVE  OF  THE  UNITED  STATES  EXPLORING  EXPEDITION.  By  CHARLES  WILKES, 
U.  S.  N.,  Commander  of  the  Expedition.     In  six  large  volumes,  imperial  quarto.     With  several 
hundred  illustrations  on  steel  and  wood,  and  numerous  large  maps.     Price  $60. 
This  is  the  same  as  the  edition  printed  for  Congress.    As  but  few  have  been  exposed  for  sale,  those  who 

desire  to  possess  this  magnificent  monument  of  the  arts  of  the  United  States,  would  do  well  to  secure  copies 

without  delay. 


PICCIOLA,  THE  PRISONER  OF  FENESTRELLA  ;  OR,  CAPTIVITY  CAPTIVE.     By  X.  B. 

SAINTINE.     New  edition,  with   illustrations.     In  one  very  neat  royal    12mo.  volume,  paper 
covers,  price  50  cents,  or  extra  cloth. 

YOUATT  AND  LEWIS  ON  THE  DOG-. 

THE  DOG.     By  William  Youatt.     Edited  by  E.  J.  Lewis,  M.D.     With  numerous  and  beautiful 
illustrations.     In  one  very  handsome  volume,  crown  Svo.,  crimson  cloth,  gilt. 


YOUATT  AND  SKINNER  ON  THE  HORSE. 

THE  HORSE.  By  William  Youatt.  A  new  edition,  with  numerous  illustrations  ;  together  with 
a  general  history  of  the  Horse  ;  a  Dissertation  on  the  American  Trotting  Horse ;  how  trained 
and  jockeyed  ;  an  Account  of  his  Remarkable  Performances  ;  and  an  Essay  on  the  Ass  and  the 
Mule.  By  J.  S.  Skinner,  Assistant  Postmaster-General,  and  Editor  of  the  Turf  Register.  In 
one  handsome  octavo  volume,  extra  cloth,  with  numerous  illustrations. 

This  edition  of  Youatt's  well-known  and  standard  work  on  the  Management,  Diseases,  and  Treatment  of 
the  Horse,  has  already  obtained  such  a  wide  circulation  throughout  the  country,  that  the  Publishers  need 
say  nothing  to  attract  to  it  the  attention  and  confidence  of  all  who  keep  Horses  or  are  interested  in  their  im- 
provement. 

THE  GARDENER'S  DICTIONARY. 

A  DICTIONARY  OF  MODERN  GARDENING.  By  G.  W.  Johnson,  Esq.  With  numerous  ad- 
ditions, by  David  Landreth.  With  one  hundred  and  eighty  wood-cuts.  In  one  very  large  royal 
12mo.  volume,  of  about  650  double-columned  pages. 

The  work  is  now  offered  at  a  very  low  price. 

THE  LANGUAGE  OF  FLOWERS,  with  Illustrative  Poetry.  To  which  are  now  added  the 
Calendar  of  Flowers,  and  the  Dial  of  Flowers.  Ninth  American,  from  the  Tenth  London  edi- 
tion. Revised  by  the  editor  of  "  Forget-me-Not.»  In  one  elegant  roval  18mo.  volume,  extra 
crimson  cloth,  gilt,  with  beautiful  colored  plates. 


BLANCHARD  &  LEA'S    MISCELLANEOUS  PUBLICATIONS.       15 
GUIZOT'S  CROMWELL— (Now  Ready.) 

HISTORY  OF  OLIYER  CROMWELL, 

AND   THE 

ENGLISH    COMMONWEALTH, 

FROM  THE  EXECUTION  OF  CHARLES  L,  TO  THE  DEATH  OF  CROMWELL, 

BY  M.   OUIZOT. 

TRANSLATED  BY  ANDREW  R.  SCOBLE. 
In  two  large  and  handsome  royal  12mo.  volumes,  extra  cloth,  containing  over  900  pages. 


To  such  a  work  as  Mr.  Guizot  has  here  assigned 
himself  he  is  eminently  competent.  Erudite,  labori- 
ous, and -accurate  ;  familiar  alike  with  the  facts  that 
constitute  the  bones  and  the  flesh  and  the  blood  of 
history,  and  the  motives  that  give  them  vitality;  at 
once  free  from  the  zealotry  of  the  bigot  and  the  indif- 
ferentism  of  the  mere  philosopher  ;  bound  to  no  parti- 
sanship and  pledged  to  no  theories  ;  he  has  enjoyed 
the  advantages  of  knowledge,  impartiality,  and  clear- 
sightedness, and  the  result  is  a  faithful  portrait  of  the 
times,  animated  with  a  wise  and  truthful  spirit,  and 


showing  in  all  its  colors  and  touches  the  hand  of  a 
skilful  master.— Philadelphia  North  American. 

We  cannot  doubt  that  this  important  work  will 
meet  with  a  hearty  and  universal  welcome.  The 
position  of  M.  Guizot,  the  circumstances  of  his  coun- 
try, and  the  interest  of  his  theme,  will  combine  to  at- 
tract towards  his  "  History  of  Cromwell"  no  ordinary 
share  of  public  curiosity.  No  Englishman  could  have 
handled  this  subject  with  more  effect,  and  M.  Guizot 
adds  new  and  valuable  matter  to  our  history. — Athe- 
ncsum. 


BUFFUM'S  SIX  MONTHS  IN  THE  GOLD  MINES;  from  a  Journal  of  Three  Years' Residence 
in  California.  In  one  royal  ISmo.  volume. 

MACKAY'S  WESTERN  WORLD,  or  Travels  in  the  United  States;  exhibiting  them  in  their 
latest  development,  Social,  Political,  and  Industrial.  In  two  neat  royal  12mo.  volumes. 

TRAVELS  IN  SIBERIA,  including  Excursions  Northward,  down  the  Obi  to  the  Polar  Circle,  and 
Southward  to  the  Chinese  Frontier.  By  ADOLPH  ERMAN.  Translated  by  WILLIAM  D.  COOLEY. 
In  two  handsome  volumes,  royal  12mo.,  extra  cloth. 

HUNGARY  AND  TRANSYLVANIA,  with  Remarks  on  their  condition,  Social,  Moral,  and  Po- 
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